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Theorem spimev 1817
Description: Distinct-variable version of spime 1704. (Contributed by NM, 5-Aug-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 1493 . 2 𝑥𝜑
2 spimev.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spime 1704 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422
This theorem is referenced by:  speiv  1818  rnxpid  4943
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