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Theorem spimev 2246
Description: Distinct-variable version of spime 2243. (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 1829 . 2 𝑥𝜑
2 spimev.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spime 2243 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033  ax-13 2233
This theorem depends on definitions:  df-bi 195  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by:  axsep  4702  dtru  4778  zfpair  4826  fvn0ssdmfun  6243  refimssco  36728  rlimdmafv  39704
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