Theorem orcom 740

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		pm1.4 739	. 2 |- ( ( ph \/ ps ) -> ( ps \/ ph ) )
2		pm1.4 739	. 2 |- ( ( ps \/ ph ) -> ( ph \/ ps ) )
3	1, 2	impbii 126	1 |- ( ( ph \/ ps ) <-> ( ps \/ ph ) )

This proof depends on syntax axioms:   <-> wb 105   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  orcomd  741  orbi1i  775  orass  779  or32  782  or42  784  orbi1d  803  pm5.61  806  oranabs  827  ordir  829  pm2.1dc  849  notnotrdc  855  dcnnOLD  861  pm5.17dc  916  pm5.7dc  967  dn1dc  973  pm5.75  975  3orrot  1015  3orcomb  1018  excxor  1427  xorcom  1437  19.33b2  1682  nf4dc  1722  nf4r  1723  19.31r  1733  dveeq2  1868  sbequilem  1891  dvelimALT  2070  dvelimfv  2071  dvelimor  2078  eueq2dc  2999  uncom  3373  reuun2  3516  prel12  3896  exmid01  4337  exmidsssnc  4342  ordtriexmid  4670  ordtri2orexmid  4672  ontr2exmid  4674  onsucsssucexmid  4676  ordsoexmid  4711  ordtri2or2exmid  4720  cnvsom  5334  fununi  5452  frec0g  6673  frecabcl  6675  frecsuclem  6682  swoer  6840  inffiexmid  7219  exmidontriimlem1  7583  enq0tr  7807  letr  8414  reapmul1  8931  reapneg  8933  reapcotr  8934  remulext1  8935  apsym  8942  mulext1  8948  elznn0nn  9667  elznn0  9668  zapne  9728  nneoor  9758  nn01to3  10032  ltxr  10193  xrletr  10226  swrdnd  11452  maxclpr  12010  minclpr  12026  odd2np1lem  12663  lcmcom  12866  dvdsprime  12924  coprm  12947  ballotfilemfc0  13289  ballotfilemfcc  13290  opprdomnbg  14691  bdbl  15746  cos11  16098  lgsdir2lem4  16372  vtxd0nedgbfi  16762  eupth2lem2dc  16922  eupth2lem3lem6fi  16934  subctctexmid  17252