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  842  pm5.71  927  prel12  4150  xpcan2  5376  funun  5561  ablfac1eulem  16687  drngmuleq0  16970  mdetunilem9  18551  maducoeval2  18571  tdeglem4  21655  deg1sublt  21708  dvply1  21876  aaliou2  21932  colline  23187  axcontlem2  23356  3orel3  27505  dfrdg4  28118  arg-ax  28399  elpell14qr2  29344  elpell1qr2  29354  jm2.22  29485  jm2.23  29486  jm2.26lem3  29491  ttac  29526  wepwsolem  29535  dgrnznn  29633  fmul01lt1lem2  29907  3ornot23VD  31886