Metamath Proof Explorer

Theorem el3v12

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 el3v12.1 
|- ( ( x e. _V /\ y e. _V /\ ch ) -> th )
Assertion el3v12 
|- ( ch -> th )

Proof

Step Hyp Ref Expression
1 el3v12.1 
 |-  ( ( x e. _V /\ y e. _V /\ ch ) -> th )
2 1 el3v1 
 |-  ( ( y e. _V /\ ch ) -> th )
3 2 el2v1 
 |-  ( ch -> th )