Theorem orc 717

Description: Introduction of a disjunct. Theorem *2.2 of [WhiteheadRussell] p. 104. (Contributed by NM, 30-Aug-1993.) (Revised by NM, 31-Jan-2015.)

Assertion

Ref	Expression
orc	|- ( ph -> ( ph \/ ps ) )

Proof of Theorem orc

Step	Hyp	Ref	Expression
1		id 19	. . 3 |- ( ( ph \/ ps ) -> ( ph \/ ps ) )
2		jaob 715	. . 3 |- ( ( ( ph \/ ps ) -> ( ph \/ ps ) ) <-> ( ( ph -> ( ph \/ ps ) ) /\ ( ps -> ( ph \/ ps ) ) ) )
3	1, 2	mpbi 145	. 2 |- ( ( ph -> ( ph \/ ps ) ) /\ ( ps -> ( ph \/ ps ) ) )
4	3	simpli 111	1 |- ( ph -> ( ph \/ ps ) )

Syntax hints:   -> wi 4   /\ wa 104   \/ wo 713

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

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm2.67-2  718  pm1.4  732  orci  736  orcd  738  orcs  740  pm2.45  743  biorfi  751  pm1.5  770  pm2.4  783  pm4.44  784  pm4.78i  787  pm4.45  789  pm3.48  790  pm2.76  813  orabs  819  ordi  821  andi  823  pm4.72  832  biort  834  dcim  846  pm2.54dc  896  pm2.85dc  910  dcor  941  pm5.71dc  967  dedlema  975  3mix1  1190  xoranor  1419  19.33  1530  hbor  1592  nford  1613  19.30dc  1673  19.43  1674  19.32r  1726  moor  2149  r19.32r  2677  ssun1  3367  undif3ss  3465  reuun1  3486  prmg  3788  opthpr  3849  exmidn0m  4284  issod  4409  elelsuc  4499  ordtri2or2exmidlem  4617  regexmidlem1  4624  fununmo  5362  nndceq  6643  nndcel  6644  swoord1  6707  swoord2  6708  exmidontri2or  7424  addlocprlem  7718  msqge0  8759  mulge0  8762  ltleap  8775  nn1m1nn  9124  elnnz  9452  zletric  9486  zlelttric  9487  zmulcl  9496  zdceq  9518  zdcle  9519  zdclt  9520  ltpnf  9972  xrlttri3  9989  xrpnfdc  10034  xrmnfdc  10035  fzdcel  10232  qletric  10456  qlelttric  10457  qdceq  10459  qdclt  10460  qsqeqor  10867  hashfiv01gt1  10999  isum  11891  iprodap  12086  iprodap0  12088  nn0o1gt2  12411  prm23lt5  12781  4sqlem17  12925  gausslemma2dlem0f  15727  bj-trdc  16074  bj-nn0suc0  16271  triap  16356  tridceq  16383