Theorem an12 561

Description: Swap two conjuncts. Note that the first digit (1) in the label refers to the outer conjunct position, and the next digit (2) to the inner conjunct position. (Contributed by NM, 12-Mar-1995.)

Assertion

Ref	Expression
an12	|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )

Proof of Theorem an12

Step	Hyp	Ref	Expression
1		ancom 266	. . 3 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	anbi1i 458	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ps /\ ph ) /\ ch ) )
3		anass 401	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
4		anass 401	. 2 |- ( ( ( ps /\ ph ) /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )
5	2, 3, 4	3bitr3i 210	1 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )

Syntax hints:   /\ wa 104   <-> wb 105

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

This theorem is referenced by:  an32  562  an13  563  an12s  565  an4  586  ceqsrexv  2933  rmoan  3003  2reuswapdc  3007  reuind  3008  2rmorex  3009  sbccomlem  3103  elunirab  3901  rexxfrd  4554  opeliunxp  4774  elres  5041  resoprab  6100  ov6g  6143  opabex3d  6266  opabex3  6267  xpassen  6989  distrnqg  7574  distrnq0  7646  rexuz2  9776  2clim  11812  bitsmod  12467  issubrg  14185  isbasis2g  14719  tgval2  14725