Theorem 3comr 1238

Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem 3comr

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3coml 1237	. 2 |- ( ( ps /\ ch /\ ph ) -> th )
3	2	3coml 1237	1 |- ( ( ch /\ ph /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ w3a 1005

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 1007

This theorem is referenced by:  nnacan  6723  le2tri3i  8347  ltaddsublt  8810  div12ap  8933  lemul12b  9100  zdivadd  9630  zdivmul  9631  elfz  10311  fzmmmeqm  10355  fzrev  10381  absdiflt  11732  absdifle  11733  dvds0lem  12442  dvdsmulc  12460  dvds2add  12466  dvds2sub  12467  dvdstr  12469  lcmdvds  12731  psmettri2  15139  xmettri2  15172