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Theorem frege63b 40780
 Description: Lemma for frege91 40826. Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege63b ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒)))

Proof of Theorem frege63b
StepHypRef Expression
1 frege62b 40779 . 2 ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒))
2 frege24 40687 . 2 (([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒)) → ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒))))
31, 2ax-mp 5 1 ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  [wsb 2069 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-12 2175  ax-frege1 40662  ax-frege2 40663  ax-frege8 40681  ax-frege58b 40773 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070 This theorem is referenced by: (None)
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