Theorem mdandyvr8

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	mdandyvr8.1	|- ( ph <-> ze )
	mdandyvr8.2	|- ( ps <-> si )
	mdandyvr8.3	|- ( ch <-> ph )
	mdandyvr8.4	|- ( th <-> ph )
	mdandyvr8.5	|- ( ta <-> ph )
	mdandyvr8.6	|- ( et <-> ps )
Assertion	mdandyvr8	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr8.1	|- ( ph <-> ze )
2		mdandyvr8.2	|- ( ps <-> si )
3		mdandyvr8.3	|- ( ch <-> ph )
4		mdandyvr8.4	|- ( th <-> ph )
5		mdandyvr8.5	|- ( ta <-> ph )
6		mdandyvr8.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvr7	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )