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Theorem dedlem0b 919
 Description: Lemma for an alternate version of weak deduction theorem. (Contributed by NM, 2-Apr-1994.)
Assertion
Ref Expression
dedlem0b φ → (ψ ↔ ((ψφ) → (χ φ))))

Proof of Theorem dedlem0b
StepHypRef Expression
1 pm2.21 100 . . . 4 φ → (φ → (χ φ)))
21imim2d 48 . . 3 φ → ((ψφ) → (ψ → (χ φ))))
32com23 72 . 2 φ → (ψ → ((ψφ) → (χ φ))))
4 pm2.21 100 . . . . 5 ψ → (ψφ))
5 simpr 447 . . . . 5 ((χ φ) → φ)
64, 5imim12i 53 . . . 4 (((ψφ) → (χ φ)) → (¬ ψφ))
76con1d 116 . . 3 (((ψφ) → (χ φ)) → (¬ φψ))
87com12 27 . 2 φ → (((ψφ) → (χ φ)) → ψ))
93, 8impbid 183 1 φ → (ψ ↔ ((ψφ) → (χ φ))))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by: (None)
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