Theorem mdandyvr13

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	mdandyvr13.1	|- ( ph <-> ze )
	mdandyvr13.2	|- ( ps <-> si )
	mdandyvr13.3	|- ( ch <-> ps )
	mdandyvr13.4	|- ( th <-> ph )
	mdandyvr13.5	|- ( ta <-> ps )
	mdandyvr13.6	|- ( et <-> ps )
Assertion	mdandyvr13	|- ( ( ( ( ch <-> si ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr13.1	|- ( ph <-> ze )
2		mdandyvr13.2	|- ( ps <-> si )
3		mdandyvr13.3	|- ( ch <-> ps )
4		mdandyvr13.4	|- ( th <-> ph )
5		mdandyvr13.5	|- ( ta <-> ps )
6		mdandyvr13.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvr2	|- ( ( ( ( ch <-> si ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )