Theorem bicomi 132

Description: Inference from commutative law for logical equivalence. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 16-Sep-2013.)

Hypothesis

Ref	Expression
bicomi.1	|- ( ph <-> ps )

Assertion

Ref	Expression
bicomi	|- ( ps <-> ph )

Proof of Theorem bicomi

Step	Hyp	Ref	Expression
1		bicomi.1	. 2 |- ( ph <-> ps )
2		bicom1 131	. 2 |- ( ( ph <-> ps ) -> ( ps <-> ph ) )
3	1, 2	ax-mp 5	1 |- ( ps <-> ph )

Syntax hints:   <-> 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:  biimpri  133  bitr2i  185  bitr3i  186  bitr4i  187  bitr3id  194  bitr3di  195  bitr4di  198  bitr4id  199  pm5.41  251  anidm  396  an21  471  pm4.87  557  anabs1  572  anabs7  574  an43  588  pm4.76  606  mtbir  675  sylnibr  681  sylnbir  683  xchnxbir  685  xchbinxr  687  nbn  704  pm4.25  763  pm4.56  785  pm4.77  804  pm3.2an3  1200  syl3anbr  1315  3an6  1356  truan  1412  truimfal  1452  nottru  1455  sbid  1820  sb10f  2046  cleljust  2206  eqabdv  2358  nfabdw  2391  necon3bbii  2437  rspc2gv  2919  alexeq  2929  ceqsrexbv  2934  clel2  2936  clel4  2939  dfsbcq2  3031  cbvreucsf  3189  dfdif3  3314  raldifb  3344  difab  3473  un0  3525  in0  3526  ss0b  3531  rexdifpr  3694  snssb  3801  snssg  3802  iindif2m  4033  epse  4433  abnex  4538  uniuni  4542  elco  4888  cotr  5110  issref  5111  mptpreima  5222  ralrnmpt  5779  rexrnmpt  5780  eroveu  6781  wrd2ind  11263  fprodseq  12102  issrg  13936  toptopon  14700  xmeterval  15117  txmetcnp  15200  dedekindicclemicc  15314  eldvap  15364  fsumdvdsmul  15673  if0ab  16193  bdeq  16210  bd0r  16212  bdcriota  16270  bj-d0clsepcl  16312  bj-dfom  16320