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	$$⊢\phi \leftrightarrow \neg \psi$$
	aiffnbandciffatnotciffb.2	$$⊢\chi \leftrightarrow \phi$$
Assertion	aiffnbandciffatnotciffb	$$⊢\neg \left(\chi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		aiffnbandciffatnotciffb.1	$$⊢\phi \leftrightarrow \neg \psi$$
2		aiffnbandciffatnotciffb.2	$$⊢\chi \leftrightarrow \phi$$
3	2 1	bitri	$$⊢\chi \leftrightarrow \neg \psi$$
4		xor3	$$⊢\neg \left(\chi \leftrightarrow \psi \right)\leftrightarrow \left(\chi \leftrightarrow \neg \psi \right)$$
5	3 4	mpbir	$$⊢\neg \left(\chi \leftrightarrow \psi \right)$$