Metamath Proof Explorer

Theorem el3v2

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 el3v2.1 
|- ( ( ph /\ y e. _V /\ ch ) -> th )
Assertion el3v2 
|- ( ( ph /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 el3v2.1 
 |-  ( ( ph /\ y e. _V /\ ch ) -> th )
2 vex 
 |-  y e. _V
3 2 1 mp3an2 
 |-  ( ( ph /\ ch ) -> th )