Theorem mdandyvrx15

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	mdandyvrx15.1	$$⊢\left(\phi ⊻\zeta \right)$$
	mdandyvrx15.2	$$⊢\left(\psi ⊻\sigma \right)$$
	mdandyvrx15.3	$$⊢\chi \leftrightarrow \psi$$
	mdandyvrx15.4	$$⊢\theta \leftrightarrow \psi$$
	mdandyvrx15.5	$$⊢\tau \leftrightarrow \psi$$
	mdandyvrx15.6	$$⊢\eta \leftrightarrow \psi$$
Assertion	mdandyvrx15	$$⊢\left(\left(\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)\wedge \left(\tau ⊻\sigma \right)\right)\wedge \left(\eta ⊻\sigma \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx15.1	$$⊢\left(\phi ⊻\zeta \right)$$
2		mdandyvrx15.2	$$⊢\left(\psi ⊻\sigma \right)$$
3		mdandyvrx15.3	$$⊢\chi \leftrightarrow \psi$$
4		mdandyvrx15.4	$$⊢\theta \leftrightarrow \psi$$
5		mdandyvrx15.5	$$⊢\tau \leftrightarrow \psi$$
6		mdandyvrx15.6	$$⊢\eta \leftrightarrow \psi$$
7	2 1 3 4 5 6	mdandyvrx0	$$⊢\left(\left(\left(\left(\chi ⊻\sigma \right)\wedge \left(\theta ⊻\sigma \right)\right)\wedge \left(\tau ⊻\sigma \right)\right)\wedge \left(\eta ⊻\sigma \right)\right)$$