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Theorem merco1lem9 1490
Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merco1lem9 ((φ → (φψ)) → (φψ))

Proof of Theorem merco1lem9
StepHypRef Expression
1 merco1lem8 1489 . 2 (( ⊥ → φ) → ((φ → (φψ)) → (φψ)))
2 merco1lem8 1489 . 2 ((( ⊥ → φ) → ((φ → (φψ)) → (φψ))) → ((φ → (φψ)) → (φψ)))
31, 2ax-mp 5 1 ((φ → (φψ)) → (φψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1317
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 177  df-tru 1319  df-fal 1320
This theorem is referenced by:  merco1lem12  1493  merco1lem14  1495  merco1lem17  1498  merco1lem18  1499  retbwax1  1500
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