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Theorem pm5.501 355
Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.501 (𝜑 → (𝜓 ↔ (𝜑𝜓)))

Proof of Theorem pm5.501
StepHypRef Expression
1 pm5.1im 252 . 2 (𝜑 → (𝜓 → (𝜑𝜓)))
2 biimp 204 . . 3 ((𝜑𝜓) → (𝜑𝜓))
32com12 32 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
41, 3impbid 201 1 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195
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 196
This theorem is referenced by:  ibib  356  ibibr  357  nbn2  359  pm5.18  370  biass  373  pm5.1  898  sadadd2lem2  14959  isclo  20649  nrmmetd  22137  bj-bibibi  31538
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