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Theorem merco1lem7 1487
 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
merco1lem7 (φ → (((ψχ) → ψ) → ψ))

Proof of Theorem merco1lem7
StepHypRef Expression
1 merco1lem5 1485 . . 3 ((((ψ → ⊥ ) → (((ψχ) → ψ) → ⊥ )) → χ) → (ψχ))
2 merco1 1478 . . 3 (((((ψ → ⊥ ) → (((ψχ) → ψ) → ⊥ )) → χ) → (ψχ)) → (((ψχ) → ψ) → (((ψχ) → ψ) → ψ)))
31, 2ax-mp 8 . 2 (((ψχ) → ψ) → (((ψχ) → ψ) → ψ))
4 merco1lem6 1486 . 2 ((((ψχ) → ψ) → (((ψχ) → ψ) → ψ)) → (φ → (((ψχ) → ψ) → ψ)))
53, 4ax-mp 8 1 (φ → (((ψχ) → ψ) → ψ))
 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:  retbwax3  1488  merco1lem17  1498
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