Theorem 3com23 1157

Description: Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Hypothesis

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

Assertion

Ref	Expression
3com23	|- ((ph /\ ch /\ ps) -> th)

Proof of Theorem 3com23

Step	Hyp	Ref	Expression
1		3exp.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3exp 1150	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com23 72	. 2 |- (ph -> (ch -> (ps -> th)))
4	3	3imp 1145	1 |- ((ph /\ ch /\ ps) -> th)

Syntax hints:   -> wi 4   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  3coml  1158  syld3an2  1229  3anidm13  1240  eqreu  3029