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Theorem pm5.501 243
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 172 . 2 (𝜑 → (𝜓 → (𝜑𝜓)))
2 bi1 117 . . 3 ((𝜑𝜓) → (𝜑𝜓))
32com12 30 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
41, 3impbid 128 1 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  ibib  244  ibibr  245  pm5.1  591  pm5.18dc  869  biassdc  1374
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