Theorem pm5.54 683

Description: Theorem *5.54 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.54	|- (((ph /\ ps) <-> ph) \/ ((ph /\ ps) <-> ps))

Proof of Theorem pm5.54

Step	Hyp	Ref	Expression
1		pm5.1 676	. . . 4 |- (((ph /\ ps) /\ ph) -> ((ph /\ ps) <-> ph))
2	1	anabss1 499	. . 3 |- ((ph /\ ps) -> ((ph /\ ps) <-> ph))
3		iba 642	. . . 4 |- (ps -> (ph <-> (ph /\ ps)))
4	3	bicomd 521	. . 3 |- (ps -> ((ph /\ ps) <-> ph))
5	2, 4	pm5.21ni 678	. 2 |- (-. ((ph /\ ps) <-> ph) -> ((ph /\ ps) <-> ps))
6	5	orri 231	1 |- (((ph /\ ps) <-> ph) \/ ((ph /\ ps) <-> ps))

Syntax hints:   <-> wb 146   \/ wo 222   /\ wa 223

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 147  df-or 224  df-an 225

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