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Theorem spc2ed 5882
 Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by Thierry Arnoux, 23-Aug-2017.)
Hypotheses
Ref Expression
spc2ed.x
spc2ed.y
spc2ed.1
Assertion
Ref Expression
spc2ed
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem spc2ed
StepHypRef Expression
1 elisset 2585 . . . 4
2 elisset 2585 . . . 4
31, 2anim12i 325 . . 3
4 eeanv 1823 . . 3
53, 4sylibr 141 . 2
6 nfv 1437 . . . . 5
7 spc2ed.x . . . . 5
86, 7nfan 1473 . . . 4
9 nfv 1437 . . . . . 6
10 spc2ed.y . . . . . 6
119, 10nfan 1473 . . . . 5
12 anass 387 . . . . . . . 8
13 ancom 257 . . . . . . . . 9
1413anbi1i 439 . . . . . . . 8
1512, 14bitr3i 179 . . . . . . 7
16 spc2ed.1 . . . . . . . 8
1716biimparc 287 . . . . . . 7
1815, 17sylbir 129 . . . . . 6
1918ex 112 . . . . 5
2011, 19eximd 1519 . . . 4
218, 20eximd 1519 . . 3
2221impancom 251 . 2
235, 22sylan2 274 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wceq 1259  wnf 1365  wex 1397   wcel 1409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by:  cnvoprab  5883
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