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Theorem frege61b 40538
Description: Lemma for frege65b 40542. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege61b (([𝑥 / 𝑦]𝜑𝜓) → (∀𝑦𝜑𝜓))

Proof of Theorem frege61b
StepHypRef Expression
1 ax-frege58b 40533 . 2 (∀𝑦𝜑 → [𝑥 / 𝑦]𝜑)
2 frege9 40444 . 2 ((∀𝑦𝜑 → [𝑥 / 𝑦]𝜑) → (([𝑥 / 𝑦]𝜑𝜓) → (∀𝑦𝜑𝜓)))
31, 2ax-mp 5 1 (([𝑥 / 𝑦]𝜑𝜓) → (∀𝑦𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  [wsb 2069
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40422  ax-frege2 40423  ax-frege8 40441  ax-frege58b 40533
This theorem is referenced by:  frege65b  40542
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