Theorem ancom31s 491

Description: Deduction rearranging conjuncts.

Hypothesis

Ref	Expression
an1rs.1	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
ancom31s	|- (((ch /\ ps) /\ ph) -> th)

Proof of Theorem ancom31s

Step	Hyp	Ref	Expression
1		an1rs.1	. . . 4 |- (((ph /\ ps) /\ ch) -> th)
2	1	exp31 376	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com13 33	. 2 |- (ch -> (ps -> (ph -> th)))
4	3	imp31 362	1 |- (((ch /\ ps) /\ ph) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  infmap1 7573  grpidinvlem3 8050  kbopt 9877  kbmult 9879  kbass2t 10050  kbass5t 10053

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 147  df-an 225

Copyright terms: Public domain