Theorem 3com13 1211

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 991	. 2 |- ( ( ch /\ ps /\ ph ) <-> ( ph /\ ps /\ ch ) )
2		3exp.1	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
3	1, 2	sylbi 121	1 |- ( ( ch /\ ps /\ ph ) -> th )

Syntax hints:   -> wi 4   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  3coml  1213  3adant3l  1237  3adant3r  1238  syld3an1  1296  oaword1  6580  nnacan  6621  elmapg  6771  subadd  8310  xrltso  9953  iooshf  10109  dvdsmulc  12245  lcmdvdsb  12521  infpnlem1  12797