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Theorem frege68c 42277
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 42218 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege59c.a . . 3 𝐴𝐵
32frege67c 42276 . 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 1540  wcel 2107  [wsbc 3744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-frege1 42136  ax-frege2 42137  ax-frege8 42155  ax-frege52a 42203  ax-frege58b 42247
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-ifp 1063  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-sbc 3745
This theorem is referenced by:  frege70  42279  frege77  42286  frege116  42325
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