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Theorem sspssr 3020
Description: Subclass in terms of proper subclass. (Contributed by Jim Kingdon, 16-Jul-2018.)
Assertion
Ref Expression
sspssr ((AB A = B) → AB)

Proof of Theorem sspssr
StepHypRef Expression
1 pssss 3016 . 2 (ABAB)
2 eqimss 2974 . 2 (A = BAB)
31, 2jaoi 623 1 ((AB A = B) → AB)
Colors of variables: wff set class
Syntax hints:  wi 4   wo 616   = wceq 1228  wss 2894  wpss 2895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908  df-pss 2910
This theorem is referenced by: (None)
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