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Theorem merco1lem15 1801
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1783. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem15 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))

Proof of Theorem merco1lem15
StepHypRef Expression
1 merco1lem14 1800 . 2 ((((𝜑𝜓) → 𝜓) → (𝜒𝜓)) → (𝜑 → (𝜒𝜓)))
2 merco1lem13 1799 . 2 (((((𝜑𝜓) → 𝜓) → (𝜒𝜓)) → (𝜑 → (𝜒𝜓))) → ((𝜑𝜓) → (𝜑 → (𝜒𝜓))))
31, 2ax-mp 5 1 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-tru 1631  df-fal 1634
This theorem is referenced by:  merco1lem16  1802  retbwax1  1805
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