Metamath Proof Explorer

Theorem el3v3

Description: New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020)

Ref Expression
Hypothesis el3v3.1 
|- ( ( ph /\ ps /\ z e. _V ) -> th )
Assertion el3v3 
|- ( ( ph /\ ps ) -> th )

Proof

Step Hyp Ref Expression
1 el3v3.1 
 |-  ( ( ph /\ ps /\ z e. _V ) -> th )
2 vex 
 |-  z e. _V
3 2 1 mp3an3 
 |-  ( ( ph /\ ps ) -> th )