Theorem el3v23 33993

Description: New way (elv 33983, el2v 33984 theorems and el3v 33987 theorems) to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.)

Hypothesis

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

Assertion

Ref	Expression
el3v23	|- ( ph -> th )

Proof of Theorem el3v23

Step	Hyp	Ref	Expression
1		el3v23.1	. . 3 |- ( ( ph /\ y e. _V /\ z e. _V ) -> th )
2	1	el3v3 33990	. 2 |- ( ( ph /\ y e. _V ) -> th )
3	2	el2v2 33986	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ w3a 1037   e. wcel 1990   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by: (None)