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Theorem pm4.44 598
Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.44 (𝜑 ↔ (𝜑 ∨ (𝜑𝜓)))

Proof of Theorem pm4.44
StepHypRef Expression
1 orc 398 . 2 (𝜑 → (𝜑 ∨ (𝜑𝜓)))
2 id 22 . . 3 (𝜑𝜑)
3 simpl 471 . . 3 ((𝜑𝜓) → 𝜑)
42, 3jaoi 392 . 2 ((𝜑 ∨ (𝜑𝜓)) → 𝜑)
51, 4impbii 197 1 (𝜑 ↔ (𝜑 ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wo 381  wa 382
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 195  df-or 383  df-an 384
This theorem is referenced by: (None)
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