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Theorem cbvralvw 2662
 Description: Version of cbvralv 2658 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.)
Hypothesis
Ref Expression
cbvralvw.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvralvw (∀𝑥𝐴 𝜑 ↔ ∀𝑦𝐴 𝜓)
Distinct variable groups:   𝑥,𝑦,𝐴   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvralvw
StepHypRef Expression
1 cbvralvw.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
21cbvralv 2658 1 (∀𝑥𝐴 𝜑 ↔ ∀𝑦𝐴 𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104  ∀wral 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422 This theorem is referenced by:  cc1  7117
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