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Theorem aiffnbandciffatnotciffb 27872
 Description: Given a is equivalent to NOT b, c is equivalent to a. there exists a proof for ( not ( c iff b ) ). (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
aiffnbandciffatnotciffb.1
aiffnbandciffatnotciffb.2
Assertion
Ref Expression
aiffnbandciffatnotciffb

Proof of Theorem aiffnbandciffatnotciffb
StepHypRef Expression
1 aiffnbandciffatnotciffb.2 . . 3
2 aiffnbandciffatnotciffb.1 . . 3
31, 2bitri 240 . 2
4 xor3 346 . . . 4
5 bicom 191 . . . . 5
65biimpi 186 . . . 4
74, 6ax-mp 8 . . 3
87biimpi 186 . 2
93, 8ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176 This theorem is referenced by:  axorbciffatcxorb  27873 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 177
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