Theorem mdandyvrx11

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	mdandyvrx11.1	|- ( ph \/_ ze )
	mdandyvrx11.2	|- ( ps \/_ si )
	mdandyvrx11.3	|- ( ch <-> ps )
	mdandyvrx11.4	|- ( th <-> ps )
	mdandyvrx11.5	|- ( ta <-> ph )
	mdandyvrx11.6	|- ( et <-> ps )
Assertion	mdandyvrx11	|- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx11.1	|- ( ph \/_ ze )
2		mdandyvrx11.2	|- ( ps \/_ si )
3		mdandyvrx11.3	|- ( ch <-> ps )
4		mdandyvrx11.4	|- ( th <-> ps )
5		mdandyvrx11.5	|- ( ta <-> ph )
6		mdandyvrx11.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvrx4	|- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ si ) )