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  3789  opthpr  3850  exmidn0m  4285  issod  4410  elelsuc  4500  ordtri2or2exmidlem  4618  regexmidlem1  4625  fununmo  5363  nndceq  6653  nndcel  6654  swoord1  6717  swoord2  6718  exmidontri2or  7439  addlocprlem  7733  msqge0  8774  mulge0  8777  ltleap  8790  nn1m1nn  9139  elnnz  9467  zletric  9501  zlelttric  9502  zmulcl  9511  zdceq  9533  zdcle  9534  zdclt  9535  ltpnf  9988  xrlttri3  10005  xrpnfdc  10050  xrmnfdc  10051  fzdcel  10248  qletric  10473  qlelttric  10474  qdceq  10476  qdclt  10477  qsqeqor  10884  hashfiv01gt1  11016  isum  11911  iprodap  12106  iprodap0  12108  nn0o1gt2  12431  prm23lt5  12801  4sqlem17  12945  gausslemma2dlem0f  15748  bj-trdc  16171  bj-nn0suc0  16368  triap  16457  tridceq  16484