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Theorem ssrexf 3159
 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 3090 . . 3
4 ssel 3091 . . . 4
54anim1d 334 . . 3
63, 5eximd 1591 . 2
7 df-rex 2422 . 2
8 df-rex 2422 . 2
96, 7, 83imtr4g 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wex 1468   wcel 1480  wnfc 2268  wrex 2417   wss 3071 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-in 3077  df-ss 3084 This theorem is referenced by: (None)
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