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Theorem pm5.21 898
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.21 ((¬ 𝜑 ∧ ¬ 𝜓) → (𝜑𝜓))

Proof of Theorem pm5.21
StepHypRef Expression
1 pm5.21im 362 . 2 𝜑 → (¬ 𝜓 → (𝜑𝜓)))
21imp 443 1 ((¬ 𝜑 ∧ ¬ 𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  onsuct0  31412  wl-nfeqfb  32301  tsbi2  32910  eliin2f  38115
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