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  6543  frecabcl  6545  frecsuclem  6552  swoer  6708  inffiexmid  7068  exmidontriimlem1  7403  enq0tr  7621  letr  8229  reapmul1  8742  reapneg  8744  reapcotr  8745  remulext1  8746  apsym  8753  mulext1  8759  elznn0nn  9460  elznn0  9461  zapne  9521  nneoor  9549  nn01to3  9812  ltxr  9971  xrletr  10004  swrdnd  11191  maxclpr  11733  minclpr  11748  odd2np1lem  12383  lcmcom  12586  dvdsprime  12644  coprm  12666  opprdomnbg  14238  bdbl  15177  cos11  15527  lgsdir2lem4  15710  subctctexmid  16366