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Theorem sspssr 3037
 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 3033 . 2 (ABAB)
2 eqimss 2991 . 2 (A = BAB)
31, 2jaoi 635 1 ((AB A = B) → AB)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 628   = wceq 1242   ⊆ wss 2911   ⊊ wpss 2912 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-pss 2927 This theorem is referenced by: (None)
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