Metamath Proof Explorer


Theorem opprc1

Description: Expansion of an ordered pair when the first member is a proper class. See also opprc . (Contributed by NM, 10-Apr-2004) (Revised by Mario Carneiro, 26-Apr-2015)

Ref Expression
Assertion opprc1 ¬ A V A B =

Proof

Step Hyp Ref Expression
1 simpl A V B V A V
2 opprc ¬ A V B V A B =
3 1 2 nsyl5 ¬ A V A B =