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Theorem frege68c 37693
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.)
Hypothesis
Ref Expression
frege59c.a 𝐴𝐵
Assertion
Ref Expression
frege68c ((∀𝑥𝜑𝜓) → (𝜓[𝐴 / 𝑥]𝜑))

Proof of Theorem frege68c
StepHypRef Expression
1 frege57aid 37634 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege59c.a . . 3 𝐴𝐵
32frege67c 37692 . 2 (((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑)) → ((∀𝑥𝜑𝜓) → (𝜓[𝐴 / 𝑥]𝜑)))
41, 3ax-mp 5 1 ((∀𝑥𝜑𝜓) → (𝜓[𝐴 / 𝑥]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478  wcel 1992  [wsbc 3422
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-12 2049  ax-ext 2606  ax-frege1 37552  ax-frege2 37553  ax-frege8 37571  ax-frege52a 37619  ax-frege58b 37663
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1012  df-tru 1483  df-fal 1486  df-ex 1702  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-v 3193  df-sbc 3423
This theorem is referenced by:  frege70  37695  frege77  37702  frege116  37741
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