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Theorem merco1lem16 1497
 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
merco1lem16 (((φ → (ψχ)) → τ) → ((φχ) → τ))

Proof of Theorem merco1lem16
StepHypRef Expression
1 merco1lem15 1496 . . 3 ((φχ) → (φ → (ψχ)))
2 merco1lem11 1492 . . 3 (((φχ) → (φ → (ψχ))) → ((((τφ) → ((φχ) → ⊥ )) → ⊥ ) → (φ → (ψχ))))
31, 2ax-mp 8 . 2 ((((τφ) → ((φχ) → ⊥ )) → ⊥ ) → (φ → (ψχ)))
4 merco1 1478 . 2 (((((τφ) → ((φχ) → ⊥ )) → ⊥ ) → (φ → (ψχ))) → (((φ → (ψχ)) → τ) → ((φχ) → τ)))
53, 4ax-mp 8 1 (((φ → (ψχ)) → τ) → ((φχ) → τ))
 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:  merco1lem17  1498  retbwax1  1500
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