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Theorem spesbcdi 33095
 Description: A lemma for introducing an existential quantifier, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.)
Hypotheses
Ref Expression
spesbcdi.1 (𝜑𝜓)
spesbcdi.2 ([𝐴 / 𝑥]𝜒𝜓)
Assertion
Ref Expression
spesbcdi (𝜑 → ∃𝑥𝜒)

Proof of Theorem spesbcdi
StepHypRef Expression
1 spesbcdi.1 . . 3 (𝜑𝜓)
2 spesbcdi.2 . . 3 ([𝐴 / 𝑥]𝜒𝜓)
31, 2sylibr 223 . 2 (𝜑[𝐴 / 𝑥]𝜒)
43spesbcd 3488 1 (𝜑 → ∃𝑥𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∃wex 1695  [wsbc 3402 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-v 3175  df-sbc 3403 This theorem is referenced by: (None)
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