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Theorem 3sstr3i 3535
 Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
3sstr3.1
3sstr3.2
3sstr3.3
Assertion
Ref Expression
3sstr3i

Proof of Theorem 3sstr3i
StepHypRef Expression
1 3sstr3.1 . 2
2 3sstr3.2 . . 3
3 3sstr3.3 . . 3
42, 3sseq12i 3523 . 2
51, 4mpbi 208 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1374   wss 3469 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-in 3476  df-ss 3483 This theorem is referenced by:  odf1o2  16382  leordtval2  19472  uniiccvol  21717  ballotlem2  28053
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