Theorem an12 563

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  564  an13  565  an12s  567  an4  588  ceqsrexv  2936  rmoan  3006  2reuswapdc  3010  reuind  3011  2rmorex  3012  sbccomlem  3106  elunirab  3906  rexxfrd  4560  opeliunxp  4781  elres  5049  resoprab  6117  ov6g  6160  opabex3d  6283  opabex3  6284  xpassen  7014  distrnqg  7607  distrnq0  7679  rexuz2  9815  2clim  11862  bitsmod  12518  issubrg  14237  isbasis2g  14771  tgval2  14777