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Theorem spesbcd 3791
 Description: form of spsbc 3711. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
spesbcd.1 (𝜑[𝐴 / 𝑥]𝜓)
Assertion
Ref Expression
spesbcd (𝜑 → ∃𝑥𝜓)

Proof of Theorem spesbcd
StepHypRef Expression
1 spesbcd.1 . 2 (𝜑[𝐴 / 𝑥]𝜓)
2 spesbc 3790 . 2 ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓)
31, 2syl 17 1 (𝜑 → ∃𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1781  [wsbc 3698 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-nfc 2901  df-ral 3075  df-rex 3076  df-v 3411  df-sbc 3699 This theorem is referenced by:  euotd  5376  ex-natded9.26  28316  bnj1465  32357  spesbcdi  35872  iscard4  40649  brtrclfv2  40836  cotrclrcl  40851
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