Theorem aistbisfiaxb

Description: Given a is equivalent to T., Given b is equivalent to F. there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016)

	Ref	Expression
Hypotheses	aistbisfiaxb.1	$$⊢\phi \leftrightarrow \top$$
	aistbisfiaxb.2	$$⊢\psi \leftrightarrow \perp$$
Assertion	aistbisfiaxb	$$⊢\left(\phi ⊻\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		aistbisfiaxb.1	$$⊢\phi \leftrightarrow \top$$
2		aistbisfiaxb.2	$$⊢\psi \leftrightarrow \perp$$
3	1	aistia	$$⊢\phi$$
4	2	aisfina	$$⊢\neg \psi$$
5	3 4	abnotbtaxb	$$⊢\left(\phi ⊻\psi \right)$$