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Theorem pm4.45im 826
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 . 2 (𝜑 → (𝜓𝜑))
21pm4.71i 563 1 (𝜑 ↔ (𝜑 ∧ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  difdif  4093
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