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Theorem spsbe 1881
Description: A specialization theorem. (Contributed by NM, 29-Jun-1993.) (Proof shortened by Wolf Lammen, 3-May-2018.)
Assertion
Ref Expression
spsbe ([𝑦 / 𝑥]𝜑 → ∃𝑥𝜑)

Proof of Theorem spsbe
StepHypRef Expression
1 sb1 1880 . 2 ([𝑦 / 𝑥]𝜑 → ∃𝑥(𝑥 = 𝑦𝜑))
2 exsimpr 1793 . 2 (∃𝑥(𝑥 = 𝑦𝜑) → ∃𝑥𝜑)
31, 2syl 17 1 ([𝑦 / 𝑥]𝜑 → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wex 1701  [wsb 1877
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-sb 1878
This theorem is referenced by:  sbft  2378  2mo  2550  bj-sbftv  32459  bj-sbfvv  32461  wl-lem-moexsb  33021  spsbce-2  38101  sb5ALT  38252  sb5ALTVD  38671
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