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Theorem intexab 5352
Description: The intersection of a nonempty class abstraction exists. (Contributed by NM, 21-Oct-2003.)
Assertion
Ref Expression
intexab (∃𝑥𝜑 {𝑥𝜑} ∈ V)

Proof of Theorem intexab
StepHypRef Expression
1 abn0 4391 . 2 ({𝑥𝜑} ≠ ∅ ↔ ∃𝑥𝜑)
2 intex 5350 . 2 ({𝑥𝜑} ≠ ∅ ↔ {𝑥𝜑} ∈ V)
31, 2bitr3i 277 1 (∃𝑥𝜑 {𝑥𝜑} ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wex 1776  wcel 2106  {cab 2712  wne 2938  Vcvv 3478  c0 4339   cint 4951
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-in 3970  df-ss 3980  df-nul 4340  df-int 4952
This theorem is referenced by:  intexrab  5353  tcmin  9779  cfval  10285  efgval  19750  relintabex  43571  rclexi  43605  rtrclex  43607  trclexi  43610  rtrclexi  43611  aiotaexb  47039
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