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Theorem exlimddvfi 30117
 Description: A lemma for eliminating an existential quantifier, in inference form. (Contributed by Giovanni Mascellani, 31-May-2019.)
Hypotheses
Ref Expression
exlimddvfi.1
exlimddvfi.2
exlimddvfi.3
exlimddvfi.4
exlimddvfi.5
exlimddvfi.6
Assertion
Ref Expression
exlimddvfi

Proof of Theorem exlimddvfi
StepHypRef Expression
1 exlimddvfi.1 . . 3
2 exlimddvfi.2 . . . . 5
32sb8e 2141 . . . 4
43bicomi 202 . . 3
51, 4sylibr 212 . 2
6 exlimddvfi.3 . 2
7 sbsbc 3328 . . . 4
8 exlimddvfi.4 . . . 4
97, 8bitri 249 . . 3
10 exlimddvfi.5 . . 3
119, 10sylanb 472 . 2
12 exlimddvfi.6 . 2
135, 6, 11, 12exlimddvf 30116 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wex 1591  wnf 1594  wsb 1706  wsbc 3324 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-sbc 3325 This theorem is referenced by: (None)
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