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Theorem ifpororb 36119
 Description: Factor conditional logic operator over disjunction in terms 2 and 3. (Contributed by RP, 21-Apr-2020.)
Assertion
Ref Expression
ifpororb if- if- if-

Proof of Theorem ifpororb
StepHypRef Expression
1 dfifp2 1422 . 2 if-
2 df-or 371 . . . 4
32imbi2i 313 . . 3
4 df-or 371 . . . 4
54imbi2i 313 . . 3
63, 5anbi12i 701 . 2
7 ifpimimb 36118 . . 3 if- if- if-
8 dfifp2 1422 . . 3 if-
9 imor 413 . . . 4 if- if- if- if-
10 ifpnot23d 36099 . . . . 5 if- if-
1110orbi1i 522 . . . 4 if- if- if- if-
129, 11bitri 252 . . 3 if- if- if- if-
137, 8, 123bitr3i 278 . 2 if- if-
141, 6, 133bitri 274 1 if- if- if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wa 370  if-wif 1420 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 188  df-or 371  df-an 372  df-ifp 1421 This theorem is referenced by:  ifpananb  36120
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