Metamath Proof Explorer


Theorem el3v23

Description: New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021)

Ref Expression
Hypothesis el3v23.1
|- ( ( ph /\ y e. _V /\ z e. _V ) -> th )
Assertion el3v23
|- ( ph -> th )

Proof

Step Hyp Ref Expression
1 el3v23.1
 |-  ( ( ph /\ y e. _V /\ z e. _V ) -> th )
2 1 el3v3
 |-  ( ( ph /\ y e. _V ) -> th )
3 2 elvd
 |-  ( ph -> th )