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Theorem ssrexf 3492
 Description: restricted existential quantification follows from a subclass relationship. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypotheses
Ref Expression
ssrexf.1
ssrexf.2
Assertion
Ref Expression
ssrexf

Proof of Theorem ssrexf
StepHypRef Expression
1 ssrexf.1 . . . 4
2 ssrexf.2 . . . 4
31, 2nfss 3425 . . 3
4 ssel 3426 . . . 4
54anim1d 568 . . 3
63, 5eximd 1960 . 2
7 df-rex 2743 . 2
8 df-rex 2743 . 2
96, 7, 83imtr4g 274 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371  wex 1663   wcel 1887  wnfc 2579  wrex 2738   wss 3404 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-in 3411  df-ss 3418 This theorem is referenced by:  iunxdif3  28175  stoweidlem34  37895
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