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Theorem pm5.1 822
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 pm5.501 370 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21biimpa 480 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  pm5.35  824  impimprbi  827  ssconb  4090  raaan  4433  raaanv  4434  raaan2  4437  suppimacnvss  7815  mdsymi  30173  tsbi1  35453  abnotbtaxb  43327  elprneb  43440
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