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Theorem eqsstr3i 2970
 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 2041 . 2 A = B
3 eqsstr3.2 . 2 B𝐶
42, 3eqsstri 2969 1 A𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1242   ⊆ wss 2911 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925 This theorem is referenced by:  inss2  3152  dmv  4494  resasplitss  5012  ofrfval  5662  fnofval  5663  ofrval  5664  off  5666  ofres  5667  ofco  5671  dftpos4  5819  smores2  5850
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