ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssexd Structured version   GIF version

Theorem ssexd 3888
Description: A subclass of a set is a set. Deduction form of ssexg 3887. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssexd.1 (φB 𝐶)
ssexd.2 (φAB)
Assertion
Ref Expression
ssexd (φA V)

Proof of Theorem ssexd
StepHypRef Expression
1 ssexd.2 . 2 (φAB)
2 ssexd.1 . 2 (φB 𝐶)
3 ssexg 3887 . 2 ((AB B 𝐶) → A V)
41, 2, 3syl2anc 391 1 (φA V)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  Vcvv 2551  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925
This theorem is referenced by:  fex2  5002  riotaexg  5415  opabbrex  5491  f1imaen2g  6209  genipv  6491
  Copyright terms: Public domain W3C validator