New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dedlema GIF version

Theorem dedlema 920
 Description: Lemma for weak deduction theorem. (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 374 . . 3 ((ψ φ) → ((ψ φ) (χ ¬ φ)))
21expcom 424 . 2 (φ → (ψ → ((ψ φ) (χ ¬ φ))))
3 simpl 443 . . . 4 ((ψ φ) → ψ)
43a1i 10 . . 3 (φ → ((ψ φ) → ψ))
5 pm2.24 101 . . . 4 (φ → (¬ φψ))
65adantld 453 . . 3 (φ → ((χ ¬ φ) → ψ))
74, 6jaod 369 . 2 (φ → (((ψ φ) (χ ¬ φ)) → ψ))
82, 7impbid 183 1 (φ → (ψ ↔ ((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-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360 This theorem is referenced by:  elimh  922  dedt  923  pm4.42  926
 Copyright terms: Public domain W3C validator