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Theorem eqsstrd 3042
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
eqsstrd.1
eqsstrd.2
Assertion
Ref Expression
eqsstrd

Proof of Theorem eqsstrd
StepHypRef Expression
1 eqsstrd.2 . 2
2 eqsstrd.1 . . 3
32sseq1d 3035 . 2
41, 3mpbird 165 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285   wss 2982 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-in 2988  df-ss 2995 This theorem is referenced by:  eqsstr3d  3043  syl6eqss  3058  tfisi  4356  suppssof1  5779  phplem4dom  6418  cardonle  6567  frecuzrdgtclt  9555
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