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Theorem dedlema 875
 Description: Lemma for iftrue 3330. (Contributed by NM, 26-Jun-2002.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
dedlema (φ → (ψ ↔ ((ψ φ) (χ ¬ φ))))

Proof of Theorem dedlema
StepHypRef Expression
1 orc 632 . . 3 ((ψ φ) → ((ψ φ) (χ ¬ φ)))
21expcom 109 . 2 (φ → (ψ → ((ψ φ) (χ ¬ φ))))
3 simpl 102 . . . 4 ((ψ φ) → ψ)
43a1i 9 . . 3 (φ → ((ψ φ) → ψ))
5 pm2.24 551 . . . 4 (φ → (¬ φψ))
65adantld 263 . . 3 (φ → ((χ ¬ φ) → ψ))
74, 6jaod 636 . 2 (φ → (((ψ φ) (χ ¬ φ)) → ψ))
82, 7impbid 120 1 (φ → (ψ ↔ ((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:  iftrue  3330
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