Theorem mdandyvrx4

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	mdandyvrx4.1	|- ( ph \/_ ze )
	mdandyvrx4.2	|- ( ps \/_ si )
	mdandyvrx4.3	|- ( ch <-> ph )
	mdandyvrx4.4	|- ( th <-> ph )
	mdandyvrx4.5	|- ( ta <-> ps )
	mdandyvrx4.6	|- ( et <-> ph )
Assertion	mdandyvrx4	|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ ze ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx4.1	|- ( ph \/_ ze )
2		mdandyvrx4.2	|- ( ps \/_ si )
3		mdandyvrx4.3	|- ( ch <-> ph )
4		mdandyvrx4.4	|- ( th <-> ph )
5		mdandyvrx4.5	|- ( ta <-> ps )
6		mdandyvrx4.6	|- ( et <-> ph )
7	1 3	axorbciffatcxorb	|- ( ch \/_ ze )
8	1 4	axorbciffatcxorb	|- ( th \/_ ze )
9	7 8	pm3.2i	|- ( ( ch \/_ ze ) /\ ( th \/_ ze ) )
10	2 5	axorbciffatcxorb	|- ( ta \/_ si )
11	9 10	pm3.2i	|- ( ( ( ch \/_ ze ) /\ ( th \/_ ze ) ) /\ ( ta \/_ si ) )
12	1 6	axorbciffatcxorb	|- ( et \/_ ze )
13	11 12	pm3.2i	|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ ze ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ ze ) )