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Theorem sseq2i 3182
Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sseq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
sseq2i (𝐶𝐴𝐶𝐵)

Proof of Theorem sseq2i
StepHypRef Expression
1 sseq1i.1 . 2 𝐴 = 𝐵
2 sseq2 3179 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wb 105   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  sseqtri  3189  sseqtrdi  3203  abss  3224  ssrab  3233  ssintrab  3867  iunpwss  3977  iotass  5194  dffun2  5225  ssimaex  5576  pw1fin  6907  pw1dc0el  6908  ss1o0el1o  6909  isstructim  12468  isstructr  12469  issubm  12795  grpissubg  12985  bj-ssom  14548  ss1oel2o  14603
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