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  2934  rmoan  3004  2reuswapdc  3008  reuind  3009  2rmorex  3010  sbccomlem  3104  elunirab  3904  rexxfrd  4558  opeliunxp  4779  elres  5047  resoprab  6112  ov6g  6155  opabex3d  6278  opabex3  6279  xpassen  7009  distrnqg  7597  distrnq0  7669  rexuz2  9805  2clim  11852  bitsmod  12507  issubrg  14225  isbasis2g  14759  tgval2  14765