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Theorem frege68c 43392
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 43333 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege59c.a . . 3 𝐴𝐵
32frege67c 43391 . 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 205  wal 1531  wcel 2098  [wsbc 3778
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699  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  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-sbc 3779
This theorem is referenced by:  frege70  43394  frege77  43401  frege116  43440
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