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Theorem axorbciffatcxorb 31595
Description: Given a is equivalent to (not b), c is equivalent to a. there exists a proof for ( c xor b ) . (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
axorbciffatcxorb.1  |-  ( ph  \/_ 
ps )
axorbciffatcxorb.2  |-  ( ch  <->  ph )
Assertion
Ref Expression
axorbciffatcxorb  |-  ( ch 
\/_  ps )

Proof of Theorem axorbciffatcxorb
StepHypRef Expression
1 axorbciffatcxorb.1 . . . . 5  |-  ( ph  \/_ 
ps )
21axorbtnotaiffb 31593 . . . 4  |-  -.  ( ph 
<->  ps )
3 xor3 357 . . . 4  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
42, 3mpbi 208 . . 3  |-  ( ph  <->  -. 
ps )
5 axorbciffatcxorb.2 . . 3  |-  ( ch  <->  ph )
64, 5aiffnbandciffatnotciffb 31594 . 2  |-  -.  ( ch 
<->  ps )
7 df-xor 1361 . 2  |-  ( ( ch  \/_  ps )  <->  -.  ( ch  <->  ps )
)
86, 7mpbir 209 1  |-  ( ch 
\/_  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1360
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-xor 1361
This theorem is referenced by:  mdandyvrx0  31648  mdandyvrx1  31649  mdandyvrx2  31650  mdandyvrx3  31651  mdandyvrx4  31652  mdandyvrx5  31653  mdandyvrx6  31654  mdandyvrx7  31655
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