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Theorem eqsstr3i 3004
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)
Hypotheses
Ref Expression
eqsstr3.1 𝐵 = 𝐴
eqsstr3.2 𝐵𝐶
Assertion
Ref Expression
eqsstr3i 𝐴𝐶

Proof of Theorem eqsstr3i
StepHypRef Expression
1 eqsstr3.1 . . 3 𝐵 = 𝐴
21eqcomi 2060 . 2 𝐴 = 𝐵
3 eqsstr3.2 . 2 𝐵𝐶
42, 3eqsstri 3003 1 𝐴𝐶
 Colors of variables: wff set class Syntax hints:   = 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:  inss2  3186  dmv  4579  resasplitss  5097  ofrfval  5748  fnofval  5749  ofrval  5750  off  5752  ofres  5753  ofco  5757  dftpos4  5909  smores2  5940  bcm1k  9628  bcpasc  9634
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