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Theorem pm5.501 242
Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 24-Jan-2013.)
Assertion
Ref Expression
pm5.501 (𝜑 → (𝜓 ↔ (𝜑𝜓)))

Proof of Theorem pm5.501
StepHypRef Expression
1 pm5.1im 171 . 2 (𝜑 → (𝜓 → (𝜑𝜓)))
2 bi1 116 . . 3 ((𝜑𝜓) → (𝜑𝜓))
32com12 30 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
41, 3impbid 127 1 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ibib  243  ibibr  244  pm5.1  566  pm5.18dc  811  biassdc  1327
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