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Theorem frege63b 41193
Description: Lemma for frege91 41239. 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 41192 . 2 ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑𝜒) → [𝑦 / 𝑥]𝜒))
2 frege24 41100 . 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 1541  [wsb 2070
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-10 2141  ax-12 2175  ax-frege1 41075  ax-frege2 41076  ax-frege8 41094  ax-frege58b 41186
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-ex 1788  df-nf 1792  df-sb 2071
This theorem is referenced by: (None)
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