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Theorem bj-sseq 13337
 Description: If two converse inclusions are characterized each by a formula, then equality is characterized by the conjunction of these formulas. (Contributed by BJ, 30-Nov-2019.)
Hypotheses
Ref Expression
bj-sseq.1
bj-sseq.2
Assertion
Ref Expression
bj-sseq

Proof of Theorem bj-sseq
StepHypRef Expression
1 bj-sseq.1 . . 3
2 bj-sseq.2 . . 3
31, 2anbi12d 465 . 2
4 eqss 3143 . 2
53, 4bitr4di 197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335   wss 3102 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-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  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-in 3108  df-ss 3115 This theorem is referenced by: (None)
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