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Theorem frege68b 37051
 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 37010 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege67b 37050 . 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 194  ∀wal 1472  [wsb 1866 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 36928  ax-frege2 36929  ax-frege8 36947  ax-frege52a 36995  ax-frege58b 37039 This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-ifp 1006  df-tru 1477  df-fal 1480 This theorem is referenced by: (None)
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