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Theorem frege68c 38727
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 38668 . 2 ((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑))
2 frege59c.a . . 3 𝐴𝐵
32frege67c 38726 . 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 1630  wcel 2139  [wsbc 3576
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-12 2196  ax-ext 2740  ax-frege1 38586  ax-frege2 38587  ax-frege8 38605  ax-frege52a 38653  ax-frege58b 38697
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ifp 1051  df-tru 1635  df-fal 1638  df-ex 1854  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-v 3342  df-sbc 3577
This theorem is referenced by:  frege70  38729  frege77  38736  frege116  38775
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