Theorem mdandyvr6

Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016)

	Ref	Expression
Hypotheses	mdandyvr6.1	|- ( ph <-> ze )
	mdandyvr6.2	|- ( ps <-> si )
	mdandyvr6.3	|- ( ch <-> ph )
	mdandyvr6.4	|- ( th <-> ps )
	mdandyvr6.5	|- ( ta <-> ps )
	mdandyvr6.6	|- ( et <-> ph )
Assertion	mdandyvr6	|- ( ( ( ( ch <-> ze ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr6.1	|- ( ph <-> ze )
2		mdandyvr6.2	|- ( ps <-> si )
3		mdandyvr6.3	|- ( ch <-> ph )
4		mdandyvr6.4	|- ( th <-> ps )
5		mdandyvr6.5	|- ( ta <-> ps )
6		mdandyvr6.6	|- ( et <-> ph )
7	3 1	bitri	|- ( ch <-> ze )
8	4 2	bitri	|- ( th <-> si )
9	7 8	pm3.2i	|- ( ( ch <-> ze ) /\ ( th <-> si ) )
10	5 2	bitri	|- ( ta <-> si )
11	9 10	pm3.2i	|- ( ( ( ch <-> ze ) /\ ( th <-> si ) ) /\ ( ta <-> si ) )
12	6 1	bitri	|- ( et <-> ze )
13	11 12	pm3.2i	|- ( ( ( ( ch <-> ze ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> ze ) )