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Theorem pm5.61 707
Description: Theorem *5.61 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 30-Jun-2013.)
Assertion
Ref Expression
pm5.61 (((φ ψ) ¬ ψ) ↔ (φ ¬ ψ))

Proof of Theorem pm5.61
StepHypRef Expression
1 biorf 662 . . 3 ψ → (φ ↔ (ψ φ)))
2 orcom 646 . . 3 ((ψ φ) ↔ (φ ψ))
31, 2syl6rbb 186 . 2 ψ → ((φ ψ) ↔ φ))
43pm5.32ri 428 1 (((φ ψ) ¬ ψ) ↔ (φ ¬ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wa 97  wb 98   wo 628
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  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.75  868  excxor  1268  xrnemnf  8469  xrnepnf  8470
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