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Theorem eqsstrri 3125
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)
Hypotheses
Ref Expression
eqsstr3.1  |-  B  =  A
eqsstr3.2  |-  B  C_  C
Assertion
Ref Expression
eqsstrri  |-  A  C_  C

Proof of Theorem eqsstrri
StepHypRef Expression
1 eqsstr3.1 . . 3  |-  B  =  A
21eqcomi 2141 . 2  |-  A  =  B
3 eqsstr3.2 . 2  |-  B  C_  C
42, 3eqsstri 3124 1  |-  A  C_  C
Colors of variables: wff set class
Syntax hints:    = wceq 1331    C_ wss 3066
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 2119
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-in 3072  df-ss 3079
This theorem is referenced by:  inss2  3292  dmv  4750  resasplitss  5297  ofrfval  5983  ofvalg  5984  ofrval  5985  off  5987  ofres  5989  ofco  5993  dftpos4  6153  smores2  6184  caseinj  6967  djuinj  6984  bcm1k  10499  bcpasc  10505
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