Theorem orcom 733

Description: Commutative law for disjunction. Theorem *4.31 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 15-Nov-2012.)

Assertion

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

Proof of Theorem orcom

Step	Hyp	Ref	Expression
1		pm1.4 732	. 2 |- ( ( ph \/ ps ) -> ( ps \/ ph ) )
2		pm1.4 732	. 2 |- ( ( ps \/ ph ) -> ( ph \/ ps ) )
3	1, 2	impbii 126	1 |- ( ( ph \/ ps ) <-> ( ps \/ ph ) )

Syntax hints:   <-> wb 105   \/ wo 713

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orcomd  734  orbi1i  768  orass  772  or32  775  or42  777  orbi1d  796  pm5.61  799  oranabs  820  ordir  822  pm2.1dc  842  notnotrdc  848  dcnnOLD  854  pm5.17dc  909  pm5.7dc  960  dn1dc  966  pm5.75  968  3orrot  1008  3orcomb  1011  excxor  1420  xorcom  1430  19.33b2  1675  nf4dc  1716  nf4r  1717  19.31r  1727  dveeq2  1861  sbequilem  1884  dvelimALT  2061  dvelimfv  2062  dvelimor  2069  eueq2dc  2976  uncom  3348  reuun2  3487  prel12  3849  exmid01  4282  exmidsssnc  4287  ordtriexmid  4613  ordtri2orexmid  4615  ontr2exmid  4617  onsucsssucexmid  4619  ordsoexmid  4654  ordtri2or2exmid  4663  cnvsom  5272  fununi  5389  frec0g  6549  frecabcl  6551  frecsuclem  6558  swoer  6716  inffiexmid  7079  exmidontriimlem1  7414  enq0tr  7632  letr  8240  reapmul1  8753  reapneg  8755  reapcotr  8756  remulext1  8757  apsym  8764  mulext1  8770  elznn0nn  9471  elznn0  9472  zapne  9532  nneoor  9560  nn01to3  9824  ltxr  9983  xrletr  10016  swrdnd  11206  maxclpr  11748  minclpr  11763  odd2np1lem  12398  lcmcom  12601  dvdsprime  12659  coprm  12681  opprdomnbg  14253  bdbl  15192  cos11  15542  lgsdir2lem4  15725  subctctexmid  16425