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Theorem pm5.33 583
Description: Theorem *5.33 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.33 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜑 ∧ ((𝜑𝜓) → 𝜒)))

Proof of Theorem pm5.33
StepHypRef Expression
1 ibar 299 . . 3 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21imbi1d 230 . 2 (𝜑 → ((𝜓𝜒) ↔ ((𝜑𝜓) → 𝜒)))
32pm5.32i 449 1 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜑 ∧ ((𝜑𝜓) → 𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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