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Theorem pm3.14 657
 Description: Theorem *3.14 of [WhiteheadRussell] p. 111. One direction of De Morgan's law). The biconditional holds for decidable propositions as seen at ianordc 792. The converse holds for decidable propositions, as seen at pm3.13dc 854. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm3.14 ((¬ φ ¬ ψ) → ¬ (φ ψ))

Proof of Theorem pm3.14
StepHypRef Expression
1 simpl 102 . . 3 ((φ ψ) → φ)
21con3i 549 . 2 φ → ¬ (φ ψ))
3 simpr 103 . . 3 ((φ ψ) → ψ)
43con3i 549 . 2 ψ → ¬ (φ ψ))
52, 4jaoi 623 1 ((¬ φ ¬ ψ) → ¬ (φ ψ))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97   ∨ wo 616 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-in1 532  ax-in2 533  ax-io 617 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  pm3.1  658  xoranor  1253  difindiss  3168
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