Theorem mdandyvrx15 41163

Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)

Hypotheses

Ref	Expression
mdandyvrx15.1	|- ( ph \/_ ze )
mdandyvrx15.2	|- ( ps \/_ si )
mdandyvrx15.3	|- ( ch <-> ps )
mdandyvrx15.4	|- ( th <-> ps )
mdandyvrx15.5	|- ( ta <-> ps )
mdandyvrx15.6	|- ( et <-> ps )

Assertion

Ref	Expression
mdandyvrx15	|- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ si ) )

Proof of Theorem mdandyvrx15

Step	Hyp	Ref	Expression
1		mdandyvrx15.2	. 2 |- ( ps \/_ si )
2		mdandyvrx15.1	. 2 |- ( ph \/_ ze )
3		mdandyvrx15.3	. 2 |- ( ch <-> ps )
4		mdandyvrx15.4	. 2 |- ( th <-> ps )
5		mdandyvrx15.5	. 2 |- ( ta <-> ps )
6		mdandyvrx15.6	. 2 |- ( et <-> ps )
7	1, 2, 3, 4, 5, 6	mdandyvrx0 41148	1 |- ( ( ( ( ch \/_ si ) /\ ( th \/_ si ) ) /\ ( ta \/_ si ) ) /\ ( et \/_ si ) )

Syntax hints:   <-> wb 196   /\ wa 384   \/_ wxo 1464

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  df-xor 1465

This theorem is referenced by: (None)