Theorem orel2 383

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)

Assertion

Ref	Expression
orel2	|- ( -. ph -> ( ( ps \/ ph ) -> ps ) )

Proof of Theorem orel2

Step	Hyp	Ref	Expression
1		idd 24	. 2 |- ( -. ph -> ( ps -> ps ) )
2		pm2.21 108	. 2 |- ( -. ph -> ( ph -> ps ) )
3	1, 2	jaod 380	1 |- ( -. ph -> ( ( ps \/ ph ) -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 368

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-or 370

This theorem is referenced by:  biorfi  407  pm2.64  787  pm2.74  844  pm5.71  934  prel12  4188  xpcan2  5430  funun  5616  ablfac1eulem  16991  drngmuleq0  17287  mdetunilem9  18989  maducoeval2  19009  tdeglem4  22324  deg1sublt  22377  dvply1  22545  aaliou2  22601  colline  23895  axcontlem2  24133  3orel3  28955  dfrdg4  29568  arg-ax  29849  elpell14qr2  30766  elpell1qr2  30776  jm2.22  30905  jm2.23  30906  jm2.26lem3  30911  ttac  30946  wepwsolem  30955  dgrnznn  31053  fmul01lt1lem2  31503  cncfiooicclem1  31599  3ornot23VD  33355