Theorem mdandyvrx3

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	mdandyvrx3.1	|- ( ph \/_ ze )
	mdandyvrx3.2	|- ( ps \/_ si )
	mdandyvrx3.3	|- ( ch <-> ps )
	mdandyvrx3.4	|- ( th <-> ps )
	mdandyvrx3.5	|- ( ta <-> ph )
	mdandyvrx3.6	|- ( et <-> ph )
Assertion	mdandyvrx3	|- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx3.1	|- ( ph \/_ ze )
2		mdandyvrx3.2	|- ( ps \/_ si )
3		mdandyvrx3.3	|- ( ch <-> ps )
4		mdandyvrx3.4	|- ( th <-> ps )
5		mdandyvrx3.5	|- ( ta <-> ph )
6		mdandyvrx3.6	|- ( et <-> ph )
7	2 3	axorbciffatcxorb	|- ( ch \/_ si )
8	2 4	axorbciffatcxorb	|- ( th \/_ si )
9	7 8	pm3.2i	|- ( ( ch \/_ si ) /\ ( th \/_ si ) )
10	1 5	axorbciffatcxorb	|- ( ta \/_ ze )
11	9 10	pm3.2i	|- ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) )
12	1 6	axorbciffatcxorb	|- ( et \/_ ze )
13	11 12	pm3.2i	|- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ ze ) )