Theorem orbi1r 1282

Description: orbi1 682 with order of disjuncts reversed. Derived from orbi1rVD 16672. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
orbi1r	|- ((ph <-> ps) -> ((ch \/ ph) <-> (ch \/ ps)))

Proof of Theorem orbi1r

Step	Hyp	Ref	Expression
1		orbi1 682	. . . 4 |- ((ph <-> ps) -> ((ph \/ ch) <-> (ps \/ ch)))
2		pm1.4 267	. . . 4 |- ((ch \/ ph) -> (ph \/ ch))
3	1, 2	syl5bi 225	. . 3 |- ((ph <-> ps) -> ((ch \/ ph) -> (ps \/ ch)))
4		pm1.4 267	. . 3 |- ((ps \/ ch) -> (ch \/ ps))
5	3, 4	syl6 25	. 2 |- ((ph <-> ps) -> ((ch \/ ph) -> (ch \/ ps)))
6		pm1.4 267	. . . 4 |- ((ch \/ ps) -> (ps \/ ch))
7	1, 6	syl5bir 227	. . 3 |- ((ph <-> ps) -> ((ch \/ ps) -> (ph \/ ch)))
8		pm1.4 267	. . 3 |- ((ph \/ ch) -> (ch \/ ph))
9	7, 8	syl6 25	. 2 |- ((ph <-> ps) -> ((ch \/ ps) -> (ch \/ ph)))
10	5, 9	impbid 574	1 |- ((ph <-> ps) -> ((ch \/ ph) <-> (ch \/ ps)))

Syntax hints:   -> wi 3   <-> wb 163   \/ wo 239

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242

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