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Theorem spimvw 1924
Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
spimvw.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
spimvw (∀𝑥𝜑𝜓)
Distinct variable groups:   𝑥,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem spimvw
StepHypRef Expression
1 ax-5 1836 . 2 𝜓 → ∀𝑥 ¬ 𝜓)
2 spimvw.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spimw 1923 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  cbvalivw  1931  alcomiw  1968  fvn0ssdmfun  6316  bj-ax9-2  32591
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