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Theorem eqrd 3146
 Description: Deduce equality of classes from equivalence of membership. (Contributed by Thierry Arnoux, 21-Mar-2017.)
Hypotheses
Ref Expression
eqrd.0
eqrd.1
eqrd.2
eqrd.3
Assertion
Ref Expression
eqrd

Proof of Theorem eqrd
StepHypRef Expression
1 eqrd.0 . . 3
2 eqrd.1 . . 3
3 eqrd.2 . . 3
4 eqrd.3 . . . 4
54biimpd 143 . . 3
61, 2, 3, 5ssrd 3133 . 2
74biimprd 157 . . 3
81, 3, 2, 7ssrd 3133 . 2
96, 8eqssd 3145 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1335  wnf 1440   wcel 2128  wnfc 2286 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-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-in 3108  df-ss 3115 This theorem is referenced by:  dfss4st  3340  imasnopn  12659
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