Theorem aisfbistiaxb

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

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

Proof

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