Theorem 3com13 1109

Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

Hypothesis

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

Assertion

Ref	Expression
3com13	|- ( ( ch /\ ps /\ ph ) -> th )

Proof of Theorem 3com13

Step	Hyp	Ref	Expression
1		3anrev 895	. 2 |- ( ( ch /\ ps /\ ph ) <-> ( ph /\ ps /\ ch ) )
2		3exp.1	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
3	1, 2	sylbi 114	1 |- ( ( ch /\ ps /\ ph ) -> th )

Syntax hints:   -> wi 4   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3coml  1111  3adant3l  1131  3adant3r  1132  syld3an1  1181  oaword1  6050  nnacan  6085  subadd  7214  xrltso  8717  iooshf  8821  elfzmlbmOLD  8989