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Theorem spesbcd 2998
Description: form of spsbc 2923. (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 2997 . 2 ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓)
31, 2syl 14 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1469  [wsbc 2912
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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-sbc 2913
This theorem is referenced by:  euotd  4183  bj-sels  13281
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