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  3368  undif3ss  3466  reuun1  3487  prmg  3792  opthpr  3853  exmidn0m  4289  issod  4414  elelsuc  4504  ordtri2or2exmidlem  4622  regexmidlem1  4629  fununmo  5369  nndceq  6662  nndcel  6663  swoord1  6726  swoord2  6727  exmidontri2or  7451  addlocprlem  7745  msqge0  8786  mulge0  8789  ltleap  8802  nn1m1nn  9151  elnnz  9479  zletric  9513  zlelttric  9514  zmulcl  9523  zdceq  9545  zdcle  9546  zdclt  9547  ltpnf  10005  xrlttri3  10022  xrpnfdc  10067  xrmnfdc  10068  fzdcel  10265  qletric  10491  qlelttric  10492  qdceq  10494  qdclt  10495  qsqeqor  10902  hashfiv01gt1  11034  isum  11936  iprodap  12131  iprodap0  12133  nn0o1gt2  12456  prm23lt5  12826  4sqlem17  12970  gausslemma2dlem0f  15773  bj-trdc  16284  bj-nn0suc0  16481  triap  16569  tridceq  16596