Theorem 3comr 1242

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 1241	. 2 |- ( ( ps /\ ch /\ ph ) -> th )
3	2	3coml 1241	1 |- ( ( ch /\ ph /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ w3a 1009

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 1011

This theorem is referenced by:  nnacan  6775  le2tri3i  8424  ltaddsublt  8889  div12ap  9014  lemul12b  9181  zdivadd  9714  zdivmul  9715  elfz  10396  fzmmmeqm  10442  fzrev  10469  absdiflt  11836  absdifle  11837  dvds0lem  12546  dvdsmulc  12564  dvds2add  12570  dvds2sub  12571  dvdstr  12573  lcmdvds  12835  psmettri2  15352  xmettri2  15385