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Theorem spsbeOLDOLD 2465
 Description: Obsolete version of spsbe 2061 as of 7-Jul-2023. A specialization theorem. (Contributed by NM, 29-Jun-1993.) (Proof shortened by Wolf Lammen, 3-May-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
spsbeOLDOLD ([𝑦 / 𝑥]𝜑 → ∃𝑥𝜑)

Proof of Theorem spsbeOLDOLD
StepHypRef Expression
1 sb1 2461 . 2 ([𝑦 / 𝑥]𝜑 → ∃𝑥(𝑥 = 𝑦𝜑))
2 exsimpr 1851 . 2 (∃𝑥(𝑥 = 𝑦𝜑) → ∃𝑥𝜑)
31, 2syl 17 1 ([𝑦 / 𝑥]𝜑 → ∃𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 396  ∃wex 1761  [wsb 2042 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-10 2112  ax-12 2141  ax-13 2344 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-ex 1762  df-nf 1766  df-sb 2043 This theorem is referenced by: (None)
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