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Theorem merco1lem4 1484
 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
merco1lem4 (((φψ) → χ) → (ψχ))

Proof of Theorem merco1lem4
StepHypRef Expression
1 merco1lem3 1483 . . 3 ((((ψ → ⊥ ) → (φ → ⊥ )) → ((χφ) → ⊥ )) → ((χφ) → (ψ → ⊥ )))
2 merco1 1478 . . 3 (((((ψ → ⊥ ) → (φ → ⊥ )) → ((χφ) → ⊥ )) → ((χφ) → (ψ → ⊥ ))) → ((((χφ) → (ψ → ⊥ )) → ψ) → (φψ)))
31, 2ax-mp 8 . 2 ((((χφ) → (ψ → ⊥ )) → ψ) → (φψ))
4 merco1 1478 . 2 (((((χφ) → (ψ → ⊥ )) → ψ) → (φψ)) → (((φψ) → χ) → (ψχ)))
53, 4ax-mp 8 1 (((φψ) → χ) → (ψχ))
 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:  merco1lem5  1485  merco1lem11  1492  merco1lem13  1494  merco1lem17  1498  merco1lem18  1499
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