Theorem mdandyvr14 41146

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
mdandyvr14.1	|- ( ph <-> ze )
mdandyvr14.2	|- ( ps <-> si )
mdandyvr14.3	|- ( ch <-> ph )
mdandyvr14.4	|- ( th <-> ps )
mdandyvr14.5	|- ( ta <-> ps )
mdandyvr14.6	|- ( et <-> ps )

Assertion

Ref	Expression
mdandyvr14	|- ( ( ( ( ch <-> ze ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )

Proof of Theorem mdandyvr14

Step	Hyp	Ref	Expression
1		mdandyvr14.2	. 2 |- ( ps <-> si )
2		mdandyvr14.1	. 2 |- ( ph <-> ze )
3		mdandyvr14.3	. 2 |- ( ch <-> ph )
4		mdandyvr14.4	. 2 |- ( th <-> ps )
5		mdandyvr14.5	. 2 |- ( ta <-> ps )
6		mdandyvr14.6	. 2 |- ( et <-> ps )
7	1, 2, 3, 4, 5, 6	mdandyvr1 41133	1 |- ( ( ( ( ch <-> ze ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( 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)