Theorem mdandyvrx12

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	mdandyvrx12.1	|- ( ph \/_ ze )
	mdandyvrx12.2	|- ( ps \/_ si )
	mdandyvrx12.3	|- ( ch <-> ph )
	mdandyvrx12.4	|- ( th <-> ph )
	mdandyvrx12.5	|- ( ta <-> ps )
	mdandyvrx12.6	|- ( et <-> ps )
Assertion	mdandyvrx12	|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ ze ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx12.1	|- ( ph \/_ ze )
2		mdandyvrx12.2	|- ( ps \/_ si )
3		mdandyvrx12.3	|- ( ch <-> ph )
4		mdandyvrx12.4	|- ( th <-> ph )
5		mdandyvrx12.5	|- ( ta <-> ps )
6		mdandyvrx12.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvrx3	|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ ze ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ si ) )