Theorem e10an 16587

Description: Conjunction form of e10 16585.

Hypotheses

Ref	Expression
e10an.1	|- . ph   ⊢   ps .
e10an.2	|- ch
e10an.3	|- ((ps /\ ch) -> th)

Assertion

Ref	Expression
e10an	|- . ph   ⊢   th .

Proof of Theorem e10an

Step	Hyp	Ref	Expression
1		e10an.1	. 2 |- . ph   ⊢   ps .
2		e10an.2	. 2 |- ch
3		e10an.3	. . 3 |- ((ps /\ ch) -> th)
4	3	ex 402	. 2 |- (ps -> (ch -> th))
5	1, 2, 4	e10 16585	1 |- . ph   ⊢   th .

Syntax hints:   -> wi 3   /\ wa 240   . vd1 16479

This theorem is referenced by:  snsslVD 16652

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-vd1 16480

Copyright terms: Public domain