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Theorem jaoi2 934
 Description: Inference removing a negated conjunct in a disjunction of an antecedent if this conjunct is part of the disjunction. (Contributed by Alexander van der Vekens, 3-Nov-2017.)
Hypothesis
Ref Expression
jaoi2.1
Assertion
Ref Expression
jaoi2

Proof of Theorem jaoi2
StepHypRef Expression
1 exmid 405 . . . 4
2 iba 490 . . . . 5
3 ancom 438 . . . . . 6
4 andir 839 . . . . . 6
53, 4bitri 241 . . . . 5
62, 5syl6bb 253 . . . 4
71, 6ax-mp 8 . . 3
87orbi2i 506 . 2
9 orass 511 . . . . 5
109bicomi 194 . . . 4
11 pm4.44 561 . . . . . 6
1211bicomi 194 . . . . 5
1312orbi1i 507 . . . 4
1410, 13bitri 241 . . 3
15 jaoi2.1 . . 3
1614, 15sylbi 188 . 2
178, 16sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359 This theorem is referenced by:  bropopvvv  6426  jaoi3  28048  2wlkonot3v  28342  2spthonot3v  28343 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
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