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Theorem eqri 23947
 Description: Infer equality of classes from equivalence of membership. (Contributed by Thierry Arnoux, 7-Oct-2017.)
Hypotheses
Ref Expression
eqri.1
eqri.2
eqri.3
Assertion
Ref Expression
eqri

Proof of Theorem eqri
StepHypRef Expression
1 nftru 1560 . . 3
2 eqri.1 . . 3
3 eqri.2 . . 3
4 eqri.3 . . . 4
54a1i 11 . . 3
61, 2, 3, 5eqrd 3326 . 2
76trud 1329 1
 Colors of variables: wff set class Syntax hints:   wb 177   wtru 1322   wceq 1649   wcel 1721  wnfc 2527 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-in 3287  df-ss 3294
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