Theorem mdandyvr3

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	mdandyvr3.1	|- ( ph <-> ze )
	mdandyvr3.2	|- ( ps <-> si )
	mdandyvr3.3	|- ( ch <-> ps )
	mdandyvr3.4	|- ( th <-> ps )
	mdandyvr3.5	|- ( ta <-> ph )
	mdandyvr3.6	|- ( et <-> ph )
Assertion	mdandyvr3	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> ze ) ) /\ ( et <-> ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr3.1	|- ( ph <-> ze )
2		mdandyvr3.2	|- ( ps <-> si )
3		mdandyvr3.3	|- ( ch <-> ps )
4		mdandyvr3.4	|- ( th <-> ps )
5		mdandyvr3.5	|- ( ta <-> ph )
6		mdandyvr3.6	|- ( et <-> ph )
7	3 2	bitri	|- ( ch <-> si )
8	4 2	bitri	|- ( th <-> si )
9	7 8	pm3.2i	|- ( ( ch <-> si ) /\ ( th <-> si ) )
10	5 1	bitri	|- ( ta <-> ze )
11	9 10	pm3.2i	|- ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> ze ) )
12	6 1	bitri	|- ( et <-> ze )
13	11 12	pm3.2i	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> ze ) ) /\ ( et <-> ze ) )