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Theorem spesbcd 3769
Description: form of spsbc 3694. (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 3768 . 2 ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓)
31, 2syl 17 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1742  [wsbc 3681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ral 3093  df-rex 3094  df-v 3417  df-sbc 3682
This theorem is referenced by:  euotd  5259  ex-natded9.26  27976  bnj1465  31770  spesbcdi  34848  brtrclfv2  39441  cotrclrcl  39456
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