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Theorem merco1lem10 1491
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem10 (((((φψ) → χ) → (τχ)) → φ) → (θφ))

Proof of Theorem merco1lem10
StepHypRef Expression
1 merco1 1478 . . 3 (((((χφ) → (τ → ⊥ )) → φ) → (φψ)) → (((φψ) → χ) → (τχ)))
2 merco1lem2 1482 . . 3 ((((((χφ) → (τ → ⊥ )) → φ) → (φψ)) → (((φψ) → χ) → (τχ))) → ((((φψ) → (θ → ⊥ )) → ((((χφ) → (τ → ⊥ )) → φ) → ⊥ )) → (((φψ) → χ) → (τχ))))
31, 2ax-mp 8 . 2 ((((φψ) → (θ → ⊥ )) → ((((χφ) → (τ → ⊥ )) → φ) → ⊥ )) → (((φψ) → χ) → (τχ)))
4 merco1 1478 . 2 (((((φψ) → (θ → ⊥ )) → ((((χφ) → (τ → ⊥ )) → φ) → ⊥ )) → (((φψ) → χ) → (τχ))) → (((((φψ) → χ) → (τχ)) → φ) → (θφ)))
53, 4ax-mp 8 1 (((((φψ) → χ) → (τχ)) → φ) → (θφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊥ wfal 1317 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-tru 1319  df-fal 1320 This theorem is referenced by:  retbwax1  1500
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