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Theorem pm4.44 696
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 633 . 2 (𝜑 → (𝜑 ∨ (𝜑𝜓)))
2 id 19 . . 3 (𝜑𝜑)
3 simpl 102 . . 3 ((𝜑𝜓) → 𝜑)
42, 3jaoi 636 . 2 ((𝜑 ∨ (𝜑𝜓)) → 𝜑)
51, 4impbii 117 1 (𝜑 ↔ (𝜑 ∨ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wa 97  wb 98  wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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