This video is a straightforward presentation on the material equivalence operator and the rules of replacement. Two statements are materially equivalent when they have the same truth value. The rules of replacement cover various complex statement forms that have the same truth value as each other. Where one appears in an argument, it may be replaced with a materially equivalent form.
I made this video from a webpage I created for the purpose. What follows is the HTML from that page minus the CSS, graphics, and title.
Material Equivalence operator
P  ≡  Q 

T  T  T 
T  F  F 
F  F  T 
F  T  F 
$p  ==  $q 

true  true  true 
true  false  false 
false  false  true 
false  true  false 
 Material Equivalence:
 (P ≡ Q) ≡ [(P ⊃ Q) & (Q ⊃ P)]
 (P ≡ Q) ≡ [(P & Q) v (~P & ~Q)]
 Double Negation:
 P ≡ ~~P
 Tautology:
 P ≡ (P & P)
 P ≡ (P v P)
 Commutation:
 (P v Q) ≡ (Q v P)
 (P & Q) ≡ (Q & P)
(x + y) = (y + x)
(x * y) = (y * x)
 Association:
 [P v (Q v R)] ≡ [(P v Q) v R]
 [P & (Q & R)] ≡ [(P & Q) & R]
(x + (y + z)) = ((x + y) + z)
(x * (y * z)) = ((x * y) * z)
 Distribution:
 [P & (Q v R)] ≡ [(P & Q) v (P & R)]
means the same as
Pat went to the dance and danced with Quentin, or Pat went to the dance and danced with Rachel.
 [P v (Q & R)] ≡ [(P v Q) & (P v R)]
means the same as
I have been to Paris or Queens, and I have been to Paris or Rome.
 De Morgan’s Theorems:
 ~(P & Q) ≡ (~P v ~Q)
means the same as
Peter is not married, or Quentin is not married.
 ~(P v Q) ≡ (~P & ~Q)
means the same as
Peter is not married, and Quentin is not married.
!($p && $q) == (!$p  !$q)
!($p  $q) == (!$p && !$q)
 Material Implication:
 (P ⊃ Q) ≡ (~P v Q)
means the same as
You will not advance your Pawn, or you will get a Queen.

if p() { q(); }
functions the same as
!p()  q();
(  P  ⊃  Q  )  ≡  (  ~  P  v  Q  ) 

T  T  T  F  T  T  T  
T  F  F  F  T  F  F  
F  T  T  T  F  T  T  
F  T  F  T  F  T  F 
 Transposition:
 (P ⊃ Q) ≡ (~Q ⊃ ~P)
P ⊃ Q ~Q So, ~P
 Exportation:
 [(P & Q) ⊃ R] ≡ [P ⊃ (Q ⊃ R)]

if ($p && $q) { run_code(); }
is logically equivalent to
if ($p) { if ($q) { run_code(); } }