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  3848  exmid01  4281  exmidsssnc  4286  ordtriexmid  4612  ordtri2orexmid  4614  ontr2exmid  4616  onsucsssucexmid  4618  ordsoexmid  4653  ordtri2or2exmid  4662  cnvsom  5271  fununi  5388  frec0g  6541  frecabcl  6543  frecsuclem  6550  swoer  6706  inffiexmid  7064  exmidontriimlem1  7399  enq0tr  7617  letr  8225  reapmul1  8738  reapneg  8740  reapcotr  8741  remulext1  8742  apsym  8749  mulext1  8755  elznn0nn  9456  elznn0  9457  zapne  9517  nneoor  9545  nn01to3  9808  ltxr  9967  xrletr  10000  swrdnd  11186  maxclpr  11728  minclpr  11743  odd2np1lem  12378  lcmcom  12581  dvdsprime  12639  coprm  12661  opprdomnbg  14232  bdbl  15171  cos11  15521  lgsdir2lem4  15704  subctctexmid  16325