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Theorem sseq2i 2998
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 2995 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 7 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wb 102   = wceq 1259  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  sseqtri  3005  syl6sseq  3019  abss  3037  ssrab  3046  ssintrab  3666  iunpwss  3771  iotass  4912  dffun2  4940  ssimaex  5262  bj-ssom  10447
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