Theorem mdandyvr15 41147

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
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

Ref	Expression
mdandyvr15	|- ( ( ( ( ch <-> si ) /\ ( th <-> si ) ) /\ ( ta <-> si ) ) /\ ( et <-> si ) )

Proof of Theorem mdandyvr15

Step	Hyp	Ref	Expression
1		mdandyvr15.2	. 2 |- ( ps <-> si )
2		mdandyvr15.1	. 2 |- ( ph <-> ze )
3		mdandyvr15.3	. 2 |- ( ch <-> ps )
4		mdandyvr15.4	. 2 |- ( th <-> ps )
5		mdandyvr15.5	. 2 |- ( ta <-> ps )
6		mdandyvr15.6	. 2 |- ( et <-> ps )
7	1, 2, 3, 4, 5, 6	mdandyvr0 41132	1 |- ( ( ( ( ch <-> si ) /\ ( 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)