Theorem mdandyvr11

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	mdandyvr11.1	|- ( ph <-> ze )
	mdandyvr11.2	|- ( ps <-> si )
	mdandyvr11.3	|- ( ch <-> ps )
	mdandyvr11.4	|- ( th <-> ps )
	mdandyvr11.5	|- ( ta <-> ph )
	mdandyvr11.6	|- ( et <-> ps )
Assertion	mdandyvr11	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr11.1	|- ( ph <-> ze )
2		mdandyvr11.2	|- ( ps <-> si )
3		mdandyvr11.3	|- ( ch <-> ps )
4		mdandyvr11.4	|- ( th <-> ps )
5		mdandyvr11.5	|- ( ta <-> ph )
6		mdandyvr11.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvr4	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )