Theorem aiffnbandciffatnotciffb

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)

	Ref	Expression
Hypotheses	aiffnbandciffatnotciffb.1	|- ( ph <-> -. ps )
	aiffnbandciffatnotciffb.2	|- ( ch <-> ph )
Assertion	aiffnbandciffatnotciffb	|- -. ( ch <-> ps )

Proof

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