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Theorem pm5.1 819
Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.1 ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem pm5.1
StepHypRef Expression
1 pm5.501 368 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21biimpa 477 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wa 396
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 208  df-an 397
This theorem is referenced by:  pm5.35  821  impimprbi  824  ssconb  4111  raaan  4456  raaanv  4457  raaan2  4460  suppimacnvss  7829  mdsymi  30115  tsbi1  35292  abnotbtaxb  43028  elprneb  43141
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