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Theorem intexabim 4009
 Description: The intersection of an inhabited class abstraction exists. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
intexabim

Proof of Theorem intexabim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 abid 2083 . . 3
21exbii 1548 . 2
3 nfsab1 2085 . . . 4
4 nfv 1473 . . . 4
5 eleq1 2157 . . . 4
63, 4, 5cbvex 1693 . . 3
7 inteximm 4006 . . 3
86, 7sylbir 134 . 2
92, 8sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1433   wcel 1445  cab 2081  cvv 2633  cint 3710 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-in 3019  df-ss 3026  df-int 3711 This theorem is referenced by:  intexrabim  4010  omex  4436
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