Theorem oel 441

Description: Elimination of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119.

Assertion

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

Proof of Theorem oel

Step	Hyp	Ref	Expression
1		orc 225	. . 3 |- (ph -> (ph \/ ps))
2	1	ancri 245	. 2 |- (ph -> ((ph \/ ps) /\ ph))
3		pm3.27 260	. 2 |- (((ph \/ ps) /\ ph) -> ph)
4	2, 3	impbi 139	1 |- (ph <-> ((ph \/ ps) /\ ph))

Syntax hints:   <-> wb 127   \/ wo 195   /\ wa 196

This theorem is referenced by:  prlem2 577

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

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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