Mathbox for Glauco Siliprandi < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ssrexf Structured version   Unicode version

Theorem ssrexf 27651
 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 3333 . . 3
4 ssel 3334 . . . 4
54anim1d 548 . . 3
63, 5eximd 1786 . 2
7 df-rex 2703 . 2
8 df-rex 2703 . 2
96, 7, 83imtr4g 262 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wcel 1725  wnfc 2558  wrex 2698   wss 3312 This theorem is referenced by:  stoweidlem34  27750 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-in 3319  df-ss 3326
 Copyright terms: Public domain W3C validator