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Theorem spimev 2397
Description: Distinct-variable version of spime 2394. (Contributed by NM, 10-Jan-1993.) Usage of this theorem is discouraged because it depends on ax-13 2377. Use spimevw 1994 instead. (New usage is discouraged.)
Hypothesis
Ref Expression
spimev.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
spimev (𝜑 → ∃𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜑(𝑦)   𝜓(𝑥,𝑦)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1914 . 2 𝑥𝜑
2 spimev.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spime 2394 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-12 2177  ax-13 2377
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-nf 1784
This theorem is referenced by: (None)
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