Theorem 3com13 1203

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 983	. 2 |- ( ( ch /\ ps /\ ph ) <-> ( ph /\ ps /\ ch ) )
2		3exp.1	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
3	1, 2	sylbi 120	1 |- ( ( ch /\ ps /\ ph ) -> th )

Syntax hints:   -> wi 4   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  3coml  1205  3adant3l  1229  3adant3r  1230  syld3an1  1279  oaword1  6450  nnacan  6491  elmapg  6639  subadd  8122  xrltso  9753  iooshf  9909  dvdsmulc  11781  lcmdvdsb  12038  infpnlem1  12311