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Theorem re1tbw1 1510
 Description: tbw-ax1 1465 rederived from merco2 1501. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw1 ((φψ) → ((ψχ) → (φχ)))

Proof of Theorem re1tbw1
StepHypRef Expression
1 mercolem8 1509 . . 3 ((φψ) → ((ψ → (φχ)) → ((φψ) → ((ψχ) → (φχ)))))
2 mercolem3 1504 . . 3 ((ψχ) → (ψ → (φχ)))
3 mercolem6 1507 . . 3 (((φψ) → ((ψ → (φχ)) → ((φψ) → ((ψχ) → (φχ))))) → ((ψ → (φχ)) → ((φψ) → ((ψχ) → (φχ)))))
41, 2, 3mpsyl 59 . 2 ((ψχ) → ((φψ) → ((ψχ) → (φχ))))
5 mercolem6 1507 . 2 (((ψχ) → ((φψ) → ((ψχ) → (φχ)))) → ((φψ) → ((ψχ) → (φχ))))
64, 5ax-mp 8 1 ((φψ) → ((ψχ) → (φχ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 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:  re1tbw4  1513
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