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Theorem eqrd 3018
 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 142 . . 3
61, 2, 3, 5ssrd 3005 . 2
74biimprd 156 . . 3
81, 3, 2, 7ssrd 3005 . 2
96, 8eqssd 3017 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wnf 1390   wcel 1434  wnfc 2207 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987 This theorem is referenced by: (None)
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