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Theorem merco1lem8 1647
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1636. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem8 (𝜑 → ((𝜓 → (𝜓𝜒)) → (𝜓𝜒)))

Proof of Theorem merco1lem8
StepHypRef Expression
1 merco1lem6 1644 . 2 ((𝜓 → (𝜓𝜒)) → ((𝜓 → (𝜓𝜒)) → (𝜓𝜒)))
2 merco1lem6 1644 . 2 (((𝜓 → (𝜓𝜒)) → ((𝜓 → (𝜓𝜒)) → (𝜓𝜒))) → (𝜑 → ((𝜓 → (𝜓𝜒)) → (𝜓𝜒))))
31, 2ax-mp 5 1 (𝜑 → ((𝜓 → (𝜓𝜒)) → (𝜓𝜒)))
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 1484  df-fal 1487
This theorem is referenced by:  merco1lem9  1648  merco1lem14  1653
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