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  2946  rmoan  3016  2reuswapdc  3020  reuind  3021  2rmorex  3022  sbccomlem  3116  elunirab  3926  rexxfrd  4583  opeliunxp  4804  elres  5073  resoprab  6148  ov6g  6191  opabex3d  6313  opabex3  6314  xpassen  7080  distrnqg  7701  distrnq0  7773  rexuz2  9912  2clim  11982  bitsmod  12638  issubrg  14358  isbasis2g  14902  tgval2  14908