Theorem el3v 33987

Description: New way (elv 33983, el2v 33984 theorems and el3v 33987 theorems) to shorten some proofs. Inference forms (with A e. _V, B e. _V and C e. _V hypotheses) of the general theorems (proving ( A e. V /\ B e. W /\ C e. X ) ->) may be superfluous. (Contributed by Peter Mazsa, 13-Oct-2018.)

Hypothesis

Ref	Expression
el3v.1	|- ( ( x e. _V /\ y e. _V /\ z e. _V ) -> ph )

Assertion

Ref	Expression
el3v	|- ph

Proof of Theorem el3v

Step	Hyp	Ref	Expression
1		vex 3203	. 2 |- x e. _V
2		vex 3203	. 2 |- y e. _V
3		vex 3203	. 2 |- z e. _V
4		el3v.1	. 2 |- ( ( x e. _V /\ y e. _V /\ z e. _V ) -> ph )
5	1, 2, 3, 4	mp3an 1424	1 |- ph

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)