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Theorem nic-mpALT 1437
 Description: A direct proof of nic-mp 1436. (Contributed by NM, 30-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-jmin φ
nic-jmaj (φ (χ ψ))
Assertion
Ref Expression
nic-mpALT ψ

Proof of Theorem nic-mpALT
StepHypRef Expression
1 nic-jmin . 2 φ
2 nic-jmaj . . . . 5 (φ (χ ψ))
3 df-nan 1288 . . . . . 6 ((φ (χ ψ)) ↔ ¬ (φ (χ ψ)))
4 df-nan 1288 . . . . . . 7 ((χ ψ) ↔ ¬ (χ ψ))
54anbi2i 675 . . . . . 6 ((φ (χ ψ)) ↔ (φ ¬ (χ ψ)))
63, 5xchbinx 301 . . . . 5 ((φ (χ ψ)) ↔ ¬ (φ ¬ (χ ψ)))
72, 6mpbi 199 . . . 4 ¬ (φ ¬ (χ ψ))
8 iman 413 . . . 4 ((φ → (χ ψ)) ↔ ¬ (φ ¬ (χ ψ)))
97, 8mpbir 200 . . 3 (φ → (χ ψ))
109simprd 449 . 2 (φψ)
111, 10ax-mp 5 1 ψ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358   ⊼ wnan 1287 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-an 360  df-nan 1288 This theorem is referenced by: (None)
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