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Theorem nbbn 347
Description: Move negation outside of biconditional. Compare Theorem *5.18 of [WhiteheadRussell] p. 124. (Contributed by NM, 27-Jun-2002.) (Proof shortened by Wolf Lammen, 20-Sep-2013.)
Assertion
Ref Expression
nbbn ((¬ φψ) ↔ ¬ (φψ))

Proof of Theorem nbbn
StepHypRef Expression
1 xor3 346 . 2 (¬ (φψ) ↔ (φ ↔ ¬ ψ))
2 con2bi 318 . 2 ((φ ↔ ¬ ψ) ↔ (ψ ↔ ¬ φ))
3 bicom 191 . 2 ((ψ ↔ ¬ φ) ↔ (¬ φψ))
41, 2, 33bitrri 263 1 ((¬ φψ) ↔ ¬ (φψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176
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 177
This theorem is referenced by:  biass  348  pclem6  896  xorass  1308  xorneg1  1311  trubifal  1351  hadbi  1387  mpto2OLD  1535
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