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Theorem frege63b 37020
Description: Lemma for frege91 37066. Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege63b ([𝑥 / 𝑦]𝜑 → (𝜓 → (∀𝑦(𝜑𝜒) → [𝑥 / 𝑦]𝜒)))

Proof of Theorem frege63b
StepHypRef Expression
1 frege62b 37019 . 2 ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑𝜒) → [𝑥 / 𝑦]𝜒))
2 frege24 36927 . 2 (([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑𝜒) → [𝑥 / 𝑦]𝜒)) → ([𝑥 / 𝑦]𝜑 → (𝜓 → (∀𝑦(𝜑𝜒) → [𝑥 / 𝑦]𝜒))))
31, 2ax-mp 5 1 ([𝑥 / 𝑦]𝜑 → (𝜓 → (∀𝑦(𝜑𝜒) → [𝑥 / 𝑦]𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  [wsb 1865
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-12 2031  ax-13 2227  ax-frege1 36902  ax-frege2 36903  ax-frege8 36921  ax-frege58b 37013
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866
This theorem is referenced by: (None)
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