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Theorem nic-idlem2 1442
 Description: Lemma for nic-id 1443. Inference used by nic-id 1443. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-idlem2.1 (η ((φ (χ ψ)) θ))
Assertion
Ref Expression
nic-idlem2 ((θ (τ (τ τ))) η)

Proof of Theorem nic-idlem2
StepHypRef Expression
1 nic-idlem2.1 . 2 (η ((φ (χ ψ)) θ))
2 nic-ax 1438 . . . 4 ((φ (χ ψ)) ((τ (τ τ)) ((φ χ) ((φ φ) (φ φ)))))
32nic-imp 1440 . . 3 ((θ (τ (τ τ))) (((φ (χ ψ)) θ) ((φ (χ ψ)) θ)))
43nic-imp 1440 . 2 ((η ((φ (χ ψ)) θ)) (((θ (τ (τ τ))) η) ((θ (τ (τ τ))) η)))
51, 4nic-mp 1436 1 ((θ (τ (τ τ))) η)
 Colors of variables: wff setvar class Syntax hints:   ⊼ wnan 1287 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  df-nan 1288 This theorem is referenced by:  nic-id  1443
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