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Theorem pm5.21 610
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.21 ((¬ φ ¬ ψ) → (φψ))

Proof of Theorem pm5.21
StepHypRef Expression
1 simpl 102 . . 3 ((¬ φ ¬ ψ) → ¬ φ)
21pm2.21d 549 . 2 ((¬ φ ¬ ψ) → (φψ))
3 simpr 103 . . 3 ((¬ φ ¬ ψ) → ¬ ψ)
43pm2.21d 549 . 2 ((¬ φ ¬ ψ) → (ψφ))
52, 4impbid 120 1 ((¬ φ ¬ ψ) → (φψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.21im  611
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