Theorem el2v2 33986

Description: New way (elv 33983, el2v 33984 theorems and el3v 33987 theorems) to shorten some proofs. (Contributed by Peter Mazsa, 23-Oct-2018.)

Hypothesis

Ref	Expression
el2v2.1	|- ( ( ph /\ y e. _V ) -> ps )

Assertion

Ref	Expression
el2v2	|- ( ph -> ps )

Proof of Theorem el2v2

Step	Hyp	Ref	Expression
1		vex 3203	. 2 |- y e. _V
2		el2v2.1	. 2 |- ( ( ph /\ y e. _V ) -> ps )
3	1, 2	mpan2 707	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   /\ wa 384   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-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:  el3v23  33993  eldm4  34037  eldmcnv  34113  ecin0  34117