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Theorem sseq2d 2950
 Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.)
Hypothesis
Ref Expression
sseq1d.1 (φA = B)
Assertion
Ref Expression
sseq2d (φ → (𝐶A𝐶B))

Proof of Theorem sseq2d
StepHypRef Expression
1 sseq1d.1 . 2 (φA = B)
2 sseq2 2944 . 2 (A = B → (𝐶A𝐶B))
31, 2syl 14 1 (φ → (𝐶A𝐶B))
 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  sseqtrd  2958  onsucsssucexmid  4196  sbcrel  4353  funimass2  4903  fnco  4933  fnssresb  4937  fnimaeq0  4946  foimacnv  5069  fvelimab  5154  ssimaexg  5160  fvmptss2  5172  rdgss  5890  frecsuclemdm  5904
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