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Theorem sseq1d 2949
Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.)
Hypothesis
Ref Expression
sseq1d.1 (φA = B)
Assertion
Ref Expression
sseq1d (φ → (A𝐶B𝐶))

Proof of Theorem sseq1d
StepHypRef Expression
1 sseq1d.1 . 2 (φA = B)
2 sseq1 2943 . 2 (A = B → (A𝐶B𝐶))
31, 2syl 14 1 (φ → (A𝐶B𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1228  wss 2894
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  sseq12d  2951  eqsstrd  2956  snssg  3474  ssiun2s  3675  treq  3834  onsucsssucexmid  4196  funimass1  4902  feq1  4956  sbcfg  4971  fvmptssdm  5180  fvimacnvi  5206  nnsucsssuc  5986  ereq1  6024
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