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Theorem aiffnbandciffatnotciffb 38210
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  |-  ( ph  <->  -. 
ps )
aiffnbandciffatnotciffb.2  |-  ( ch  <->  ph )
Assertion
Ref Expression
aiffnbandciffatnotciffb  |-  -.  ( ch 
<->  ps )

Proof of Theorem aiffnbandciffatnotciffb
StepHypRef Expression
1 aiffnbandciffatnotciffb.2 . . 3  |-  ( ch  <->  ph )
2 aiffnbandciffatnotciffb.1 . . 3  |-  ( ph  <->  -. 
ps )
31, 2bitri 253 . 2  |-  ( ch  <->  -. 
ps )
4 xor3 359 . 2  |-  ( -.  ( ch  <->  ps )  <->  ( ch  <->  -.  ps )
)
53, 4mpbir 213 1  |-  -.  ( ch 
<->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 188
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 189
This theorem is referenced by:  axorbciffatcxorb  38211
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