Theorem mdandyvr15

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	mdandyvr15.1	|- ( ph <-> ze )
	mdandyvr15.2	|- ( ps <-> si )
	mdandyvr15.3	|- ( ch <-> ps )
	mdandyvr15.4	|- ( th <-> ps )
	mdandyvr15.5	|- ( ta <-> ps )
	mdandyvr15.6	|- ( et <-> ps )
Assertion	mdandyvr15	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr15.1	|- ( ph <-> ze )
2		mdandyvr15.2	|- ( ps <-> si )
3		mdandyvr15.3	|- ( ch <-> ps )
4		mdandyvr15.4	|- ( th <-> ps )
5		mdandyvr15.5	|- ( ta <-> ps )
6		mdandyvr15.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvr0	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )