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Theorem eqssd 2956
Description: Equality deduction from two subclass relationships. Compare Theorem 4 of [Suppes] p. 22. (Contributed by NM, 27-Jun-2004.)
Hypotheses
Ref Expression
eqssd.1  C_
eqssd.2  C_
Assertion
Ref Expression
eqssd

Proof of Theorem eqssd
StepHypRef Expression
1 eqssd.1 . 2  C_
2 eqssd.2 . 2  C_
3 eqss 2954 . 2 
C_  C_
41, 2, 3sylanbrc 394 1
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242    C_ 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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  eqrd  2957  unissel  3600  intmin  3626  int0el  3636  dmcosseq  4546  relfld  4789  imadif  4922  imain  4924  fimacnv  5239  fo2ndf  5790  tposeq  5803  tfrlemibfn  5883  tfrlemi14d  5888  addnqpr1  6541  distrprg  6562  ltexpri  6585  addcanprg  6588  recexprlemex  6607  aptipr  6611  fzopth  8654  fzosplit  8763  fzouzsplit  8765  frecuzrdgfn  8839  findset  9333
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