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Theorem bj-spimevv 32847
Description: Version of spimev 2295 with a dv condition, which does not require ax-13 2282. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-spimevv.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-spimevv (𝜑 → ∃𝑥𝜓)
Distinct variable groups:   𝑥,𝑦   𝜑,𝑥
Allowed substitution hints:   𝜑(𝑦)   𝜓(𝑥,𝑦)

Proof of Theorem bj-spimevv
StepHypRef Expression
1 nfv 1883 . 2 𝑥𝜑
2 bj-spimevv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2bj-spimev 32845 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1744
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  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-tru 1526  df-ex 1745  df-nf 1750
This theorem is referenced by:  bj-axsep  32918  bj-dtru  32922
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