Theorem 3comr 1213

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 1212	. 2 |- ( ( ps /\ ch /\ ph ) -> th )
3	2	3coml 1212	1 |- ( ( ch /\ ph /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ w3a 980

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 982

This theorem is referenced by:  nnacan  6579  le2tri3i  8152  ltaddsublt  8615  div12ap  8738  lemul12b  8905  zdivadd  9432  zdivmul  9433  elfz  10106  fzmmmeqm  10150  fzrev  10176  absdiflt  11274  absdifle  11275  dvds0lem  11983  dvdsmulc  12001  dvds2add  12007  dvds2sub  12008  dvdstr  12010  lcmdvds  12272  psmettri2  14648  xmettri2  14681