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Theorem dedlemb 921
 Description: Lemma for weak deduction theorem. (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 373 . . 3 ((χ ¬ φ) → ((ψ φ) (χ ¬ φ)))
21expcom 424 . 2 φ → (χ → ((ψ φ) (χ ¬ φ))))
3 pm2.21 100 . . . 4 φ → (φχ))
43adantld 453 . . 3 φ → ((ψ φ) → χ))
5 simpl 443 . . . 4 ((χ ¬ φ) → χ)
65a1i 10 . . 3 φ → ((χ ¬ φ) → χ))
74, 6jaod 369 . 2 φ → (((ψ φ) (χ ¬ φ)) → χ))
82, 7impbid 183 1 φ → (χ ↔ ((ψ φ) (χ ¬ φ))))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357   ∧ wa 358 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  df-or 359  df-an 360 This theorem is referenced by:  elimh  922  pm4.42  926  iffalse  3669
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