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Theorem dfss1 3285
 Description: A frequently-used variant of subclass definition df-ss 3089. (Contributed by NM, 10-Jan-2015.)
Assertion
Ref Expression
dfss1 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)

Proof of Theorem dfss1
StepHypRef Expression
1 df-ss 3089 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
2 incom 3273 . . 3 (𝐴𝐵) = (𝐵𝐴)
32eqeq1i 2148 . 2 ((𝐴𝐵) = 𝐴 ↔ (𝐵𝐴) = 𝐴)
41, 3bitri 183 1 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1332   ∩ cin 3075   ⊆ wss 3076 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082  df-ss 3089 This theorem is referenced by:  dfss5  3286  sseqin2  3300  onintexmid  4495  xpimasn  4995  fndmdif  5533  infiexmid  6779  ssfidc  6831  isumss  11193  znnen  11948
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