Theorem mdandyvrx7

Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016)

	Ref	Expression
Hypotheses	mdandyvrx7.1	$$⊢\left(\phi ⊻\zeta \right)$$
	mdandyvrx7.2	$$⊢\left(\psi ⊻\sigma \right)$$
	mdandyvrx7.3	$$⊢\chi \leftrightarrow \psi$$
	mdandyvrx7.4	$$⊢\theta \leftrightarrow \psi$$
	mdandyvrx7.5	$$⊢\tau \leftrightarrow \psi$$
	mdandyvrx7.6	$$⊢\eta \leftrightarrow \phi$$
Assertion	mdandyvrx7	$$⊢\left(\left(\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)\wedge \left(\tau ⊻\sigma \right)\right)\wedge \left(\eta ⊻\zeta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx7.1	$$⊢\left(\phi ⊻\zeta \right)$$
2		mdandyvrx7.2	$$⊢\left(\psi ⊻\sigma \right)$$
3		mdandyvrx7.3	$$⊢\chi \leftrightarrow \psi$$
4		mdandyvrx7.4	$$⊢\theta \leftrightarrow \psi$$
5		mdandyvrx7.5	$$⊢\tau \leftrightarrow \psi$$
6		mdandyvrx7.6	$$⊢\eta \leftrightarrow \phi$$
7	2 3	axorbciffatcxorb	$$⊢\left(\chi ⊻\sigma \right)$$
8	2 4	axorbciffatcxorb	$$⊢\left(\theta ⊻\sigma \right)$$
9	7 8	pm3.2i	$$⊢\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)$$
10	2 5	axorbciffatcxorb	$$⊢\left(\tau ⊻\sigma \right)$$
11	9 10	pm3.2i	$$⊢\left(\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)\wedge \left(\tau ⊻\sigma \right)\right)$$
12	1 6	axorbciffatcxorb	$$⊢\left(\eta ⊻\zeta \right)$$
13	11 12	pm3.2i	$$⊢\left(\left(\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)\wedge \left(\tau ⊻\sigma \right)\right)\wedge \left(\eta ⊻\zeta \right)\right)$$