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Theorem pm4.43 855
Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Assertion
Ref Expression
pm4.43 (φ ↔ ((φ ψ) (φ ¬ ψ)))

Proof of Theorem pm4.43
StepHypRef Expression
1 pm3.24 626 . . 3 ¬ (ψ ¬ ψ)
21biorfi 664 . 2 (φ ↔ (φ (ψ ¬ ψ)))
3 ordi 728 . 2 ((φ (ψ ¬ ψ)) ↔ ((φ ψ) (φ ¬ ψ)))
42, 3bitri 173 1 (φ ↔ ((φ 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-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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