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Theorem pm5.1 824
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 pm5.501 366 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21biimpa 476 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395
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 207  df-an 396
This theorem is referenced by:  pm5.35  826  impimprbi  829  ssconb  4152  raaan  4523  raaanv  4524  raaan2  4527  suppimacnvss  8197  mdsymi  32440  ply1degltel  33595  ply1degleel  33596  tsbi1  38120  abnotbtaxb  46865  elprneb  46979
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