Metamath Proof Explorer


Theorem aovpcov0

Description: If the alternative value of the operation on an ordered pair is the universal class, the operation's value at this ordered pair is the empty set. (Contributed by Alexander van der Vekens, 26-May-2017)

Ref Expression
Assertion aovpcov0 A F B = V A F B =

Proof

Step Hyp Ref Expression
1 afvpcfv0 F ''' A B = V F A B =
2 df-aov A F B = F ''' A B
3 2 eqeq1i A F B = V F ''' A B = V
4 df-ov A F B = F A B
5 4 eqeq1i A F B = F A B =
6 1 3 5 3imtr4i A F B = V A F B =