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Theorem bj-chvarvv 32851
Description: Version of chvarv 2299 with a dv condition, which does not require ax-13 2282. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-chvarvv.1 (𝑥 = 𝑦 → (𝜑𝜓))
bj-chvarvv.2 𝜑
Assertion
Ref Expression
bj-chvarvv 𝜓
Distinct variable groups:   𝑥,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem bj-chvarvv
StepHypRef Expression
1 bj-chvarvv.1 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
21bj-spvv 32848 . 2 (∀𝑥𝜑𝜓)
3 bj-chvarvv.2 . 2 𝜑
42, 3mpg 1764 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196
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:  bj-axext3  32894  bj-axrep1  32913  bj-axsep2  33046
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