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Theorem lukshefth1 1460
 Description: Lemma for renicax 1462. (Contributed by NM, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
lukshefth1 ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ)))

Proof of Theorem lukshefth1
StepHypRef Expression
1 lukshef-ax1 1459 . 2 ((φ (ψ χ)) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ)))))
2 lukshef-ax1 1459 . . . 4 ((τ (τ τ)) ((θ (θ θ)) ((θ τ) ((τ θ) (τ θ)))))
3 lukshef-ax1 1459 . . . 4 (((τ (τ τ)) ((θ (θ θ)) ((θ τ) ((τ θ) (τ θ))))) ((((τ ψ) ((φ τ) (φ τ))) (((τ ψ) ((φ τ) (φ τ))) ((τ ψ) ((φ τ) (φ τ))))) ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ)))) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ))))))))
42, 3nic-mp 1436 . . 3 ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ)))) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ))))))
5 lukshef-ax1 1459 . . 3 (((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ)))) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ)))))) (((φ (ψ χ)) ((φ (ψ χ)) (φ (ψ χ)))) (((φ (ψ χ)) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ))))) (((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ))) ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ)))))))
64, 5nic-mp 1436 . 2 (((φ (ψ χ)) ((τ (τ τ)) ((τ ψ) ((φ τ) (φ τ))))) (((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ))) ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ)))))
71, 6nic-mp 1436 1 ((((τ ψ) ((φ τ) (φ τ))) (θ (θ θ))) (φ (ψ χ)))
 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:  lukshefth2  1461  renicax  1462
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