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Theorem pm4.45im 545
Description: Conjunction with implication. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
pm4.45im (φ ↔ (φ (ψφ)))

Proof of Theorem pm4.45im
StepHypRef Expression
1 ax-1 6 . . 3 (φ → (ψφ))
21ancli 534 . 2 (φ → (φ (ψφ)))
3 simpl 443 . 2 ((φ (ψφ)) → φ)
42, 3impbii 180 1 (φ ↔ (φ (ψφ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   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-an 360
This theorem is referenced by:  difdif  3393
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