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Theorem eqsstrri 3130
 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
eqsstrri 𝐴𝐶

Proof of Theorem eqsstrri
StepHypRef Expression
1 eqsstr3.1 . . 3 𝐵 = 𝐴
21eqcomi 2143 . 2 𝐴 = 𝐵
3 eqsstr3.2 . 2 𝐵𝐶
42, 3eqsstri 3129 1 𝐴𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ⊆ wss 3071 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084 This theorem is referenced by:  inss2  3297  dmv  4755  resasplitss  5302  ofrfval  5990  ofvalg  5991  ofrval  5992  off  5994  ofres  5996  ofco  6000  dftpos4  6160  smores2  6191  caseinj  6974  djuinj  6991  bcm1k  10518  bcpasc  10524
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