Theorem 3comr 1214

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 1213	. 2 |- ( ( ps /\ ch /\ ph ) -> th )
3	2	3coml 1213	1 |- ( ( ch /\ ph /\ ps ) -> 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:  nnacan  6598  le2tri3i  8181  ltaddsublt  8644  div12ap  8767  lemul12b  8934  zdivadd  9462  zdivmul  9463  elfz  10136  fzmmmeqm  10180  fzrev  10206  absdiflt  11403  absdifle  11404  dvds0lem  12112  dvdsmulc  12130  dvds2add  12136  dvds2sub  12137  dvdstr  12139  lcmdvds  12401  psmettri2  14800  xmettri2  14833