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Theorem renicax 1462
 Description: A rederivation of nic-ax 1438 from lukshef-ax1 1459, proving that lukshef-ax1 1459 with nic-mp 1436 can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
renicax ((φ (χ ψ)) ((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))))

Proof of Theorem renicax
StepHypRef Expression
1 lukshefth1 1460 . . . 4 ((((θ χ) ((φ θ) (φ θ))) (τ (τ τ))) (φ (χ ψ)))
2 lukshefth2 1461 . . . 4 (((((θ χ) ((φ θ) (φ θ))) (τ (τ τ))) (φ (χ ψ))) (((φ (χ ψ)) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ)))) ((φ (χ ψ)) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ))))))
31, 2nic-mp 1436 . . 3 ((φ (χ ψ)) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ))))
4 lukshefth2 1461 . . . 4 (((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) ((((θ χ) ((φ θ) (φ θ))) (τ (τ τ))) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ)))))
5 lukshef-ax1 1459 . . . 4 ((((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) ((((θ χ) ((φ θ) (φ θ))) (τ (τ τ))) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ))))) (((φ (χ ψ)) ((φ (χ ψ)) (φ (χ ψ)))) (((φ (χ ψ)) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ)))) ((((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ))) (((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ)))))))
64, 5nic-mp 1436 . . 3 (((φ (χ ψ)) (((θ χ) ((φ θ) (φ θ))) (τ (τ τ)))) ((((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ))) (((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ)))))
73, 6nic-mp 1436 . 2 (((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ)))
8 lukshefth2 1461 . 2 ((((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))) (φ (χ ψ))) (((φ (χ ψ)) ((τ (τ τ)) ((θ χ) ((φ θ) (φ θ))))) ((φ (χ ψ)) ((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))))))
97, 8nic-mp 1436 1 ((φ (χ ψ)) ((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))))
 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: (None)
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