Theorem mdandyvr9 41141

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.)

Hypotheses

Ref	Expression
mdandyvr9.1	|- ( ph <-> ze )
mdandyvr9.2	|- ( ps <-> si )
mdandyvr9.3	|- ( ch <-> ps )
mdandyvr9.4	|- ( th <-> ph )
mdandyvr9.5	|- ( ta <-> ph )
mdandyvr9.6	|- ( et <-> ps )

Assertion

Ref	Expression
mdandyvr9	|- ( ( ( ( ch <-> si ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )

Proof of Theorem mdandyvr9

Step	Hyp	Ref	Expression
1		mdandyvr9.2	. 2 |- ( ps <-> si )
2		mdandyvr9.1	. 2 |- ( ph <-> ze )
3		mdandyvr9.3	. 2 |- ( ch <-> ps )
4		mdandyvr9.4	. 2 |- ( th <-> ph )
5		mdandyvr9.5	. 2 |- ( ta <-> ph )
6		mdandyvr9.6	. 2 |- ( et <-> ps )
7	1, 2, 3, 4, 5, 6	mdandyvr6 41138	1 |- ( ( ( ( ch <-> si ) /\ ( th <-> ze ) ) /\ ( ta <-> ze ) ) /\ ( et <-> si ) )

Syntax hints:   <-> wb 196   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)