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Theorem spimev 2295
 Description: Distinct-variable version of spime 2292. (Contributed by NM, 10-Jan-1993.)
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 1883 . 2 𝑥𝜑
2 spimev.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spime 2292 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  ax-13 2282 This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750 This theorem is referenced by:  axsep  4813  dtru  4887  zfpair  4934  fvn0ssdmfun  6390  refimssco  38230  rlimdmafv  41578  elsprel  42050
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