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Theorem merco1lem2 1482
 Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem2 (((φψ) → χ) → (((ψτ) → (φ → ⊥ )) → χ))

Proof of Theorem merco1lem2
StepHypRef Expression
1 retbwax2 1481 . . 3 ((((ψτ) → (φ → ⊥ )) → ⊥ ) → ((χφ) → (((ψτ) → (φ → ⊥ )) → ⊥ )))
2 merco1 1478 . . 3 (((((ψτ) → (φ → ⊥ )) → ⊥ ) → ((χφ) → (((ψτ) → (φ → ⊥ )) → ⊥ ))) → ((((χφ) → (((ψτ) → (φ → ⊥ )) → ⊥ )) → ψ) → (φψ)))
31, 2ax-mp 8 . 2 ((((χφ) → (((ψτ) → (φ → ⊥ )) → ⊥ )) → ψ) → (φψ))
4 merco1 1478 . 2 (((((χφ) → (((ψτ) → (φ → ⊥ )) → ⊥ )) → ψ) → (φψ)) → (((φψ) → χ) → (((ψτ) → (φ → ⊥ )) → χ)))
53, 4ax-mp 8 1 (((φψ) → χ) → (((ψτ) → (φ → ⊥ )) → χ))
 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:  merco1lem3  1483  merco1lem10  1491  merco1lem11  1492  merco1lem18  1499
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