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Theorem cbvalivw 1980
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
cbvalivw.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvalivw (∀𝑥𝜑 → ∀𝑦𝜓)
Distinct variable groups:   𝑥,𝑦   𝜓,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvalivw
StepHypRef Expression
1 cbvalivw.1 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
21spimvw 1973 . 2 (∀𝑥𝜑𝜓)
32alrimiv 1895 1 (∀𝑥𝜑 → ∀𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1521 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945 This theorem depends on definitions:  df-bi 197  df-ex 1745 This theorem is referenced by:  alcomiw  2013  cbvaev  2021  axc11next  38924
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