Theorem aiffnbandciffatnotciffb 41071

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

Step	Hyp	Ref	Expression
1		aiffnbandciffatnotciffb.2	. . 3 |- ( ch <-> ph )
2		aiffnbandciffatnotciffb.1	. . 3 |- ( ph <-> -. ps )
3	1, 2	bitri 264	. 2 |- ( ch <-> -. ps )
4		xor3 372	. 2 |- ( -. ( ch <-> ps ) <-> ( ch <-> -. ps ) )
5	3, 4	mpbir 221	1 |- -. ( ch <-> ps )

Syntax hints:   -. wn 3   <-> wb 196

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 197

This theorem is referenced by:  axorbciffatcxorb  41072