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Theorem pm4.44 560
Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.44 (φ ↔ (φ (φ ψ)))

Proof of Theorem pm4.44
StepHypRef Expression
1 orc 374 . 2 (φ → (φ (φ ψ)))
2 id 19 . . 3 (φφ)
3 simpl 443 . . 3 ((φ ψ) → φ)
42, 3jaoi 368 . 2 ((φ (φ ψ)) → φ)
51, 4impbii 180 1 (φ ↔ (φ (φ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357   wa 358
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 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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