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Theorem frege68b 43374
Description: Combination of applying a definition and applying it to a specific instance. Proposition 68 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege68b ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑))

Proof of Theorem frege68b
StepHypRef Expression
1 frege57aid 43333 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege67b 43373 . 2 (((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑)) → ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑)))
31, 2ax-mp 5 1 ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wal 1531  [wsb 2059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 43251  ax-frege2 43252  ax-frege8 43270  ax-frege52a 43318  ax-frege58b 43362
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-ifp 1061  df-tru 1536  df-fal 1546
This theorem is referenced by: (None)
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