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Theorem dedlemb 876
Description: Lemma for iffalse 3333. (Contributed by NM, 15-May-1999.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
dedlemb φ → (χ ↔ ((ψ φ) (χ ¬ φ))))

Proof of Theorem dedlemb
StepHypRef Expression
1 olc 631 . . 3 ((χ ¬ φ) → ((ψ φ) (χ ¬ φ)))
21expcom 109 . 2 φ → (χ → ((ψ φ) (χ ¬ φ))))
3 pm2.21 547 . . . 4 φ → (φχ))
43adantld 263 . . 3 φ → ((ψ φ) → χ))
5 simpl 102 . . . 4 ((χ ¬ φ) → χ)
65a1i 9 . . 3 φ → ((χ ¬ φ) → χ))
74, 6jaod 636 . 2 φ → (((ψ φ) (χ ¬ φ)) → χ))
82, 7impbid 120 1 φ → (χ ↔ ((ψ φ) (χ ¬ φ))))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   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:  iffalse  3333
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