Theorem mdandyvr4

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	mdandyvr4.1	|- ( ph <-> ze )
	mdandyvr4.2	|- ( ps <-> si )
	mdandyvr4.3	|- ( ch <-> ph )
	mdandyvr4.4	|- ( th <-> ph )
	mdandyvr4.5	|- ( ta <-> ps )
	mdandyvr4.6	|- ( et <-> ph )
Assertion	mdandyvr4	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr4.1	|- ( ph <-> ze )
2		mdandyvr4.2	|- ( ps <-> si )
3		mdandyvr4.3	|- ( ch <-> ph )
4		mdandyvr4.4	|- ( th <-> ph )
5		mdandyvr4.5	|- ( ta <-> ps )
6		mdandyvr4.6	|- ( et <-> ph )
7	3 1	bitri	|- ( ch <-> ze )
8	4 1	bitri	|- ( th <-> ze )
9	7 8	pm3.2i	|- ( ( ch <-> ze ) /\ ( th <-> ze ) )
10	5 2	bitri	|- ( ta <-> si )
11	9 10	pm3.2i	|- ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) )
12	6 1	bitri	|- ( et <-> ze )
13	11 12	pm3.2i	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> ze ) )