Theorem mdandyvr12

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	mdandyvr12.1	|- ( ph <-> ze )
	mdandyvr12.2	|- ( ps <-> si )
	mdandyvr12.3	|- ( ch <-> ph )
	mdandyvr12.4	|- ( th <-> ph )
	mdandyvr12.5	|- ( ta <-> ps )
	mdandyvr12.6	|- ( et <-> ps )
Assertion	mdandyvr12	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr12.1	|- ( ph <-> ze )
2		mdandyvr12.2	|- ( ps <-> si )
3		mdandyvr12.3	|- ( ch <-> ph )
4		mdandyvr12.4	|- ( th <-> ph )
5		mdandyvr12.5	|- ( ta <-> ps )
6		mdandyvr12.6	|- ( et <-> ps )
7	2 1 3 4 5 6	mdandyvr3	|- ( ( ( ( ch <-> ze ) /\ ( th <-> ze ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )