Theorem mdandyvr0

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	mdandyvr0.1	|- ( ph <-> ze )
	mdandyvr0.2	|- ( ps <-> si )
	mdandyvr0.3	|- ( ch <-> ph )
	mdandyvr0.4	|- ( th <-> ph )
	mdandyvr0.5	|- ( ta <-> ph )
	mdandyvr0.6	|- ( et <-> ph )
Assertion	mdandyvr0	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> ze ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr0.1	|- ( ph <-> ze )
2		mdandyvr0.2	|- ( ps <-> si )
3		mdandyvr0.3	|- ( ch <-> ph )
4		mdandyvr0.4	|- ( th <-> ph )
5		mdandyvr0.5	|- ( ta <-> ph )
6		mdandyvr0.6	|- ( 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 1	bitri	|- ( ta <-> ze )
11	9 10	pm3.2i	|- ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) )
12	6 1	bitri	|- ( et <-> ze )
13	11 12	pm3.2i	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> ze ) )