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Theorem dfss1 3460
 Description: A frequently-used variant of subclass definition df-ss 3259. (Contributed by NM, 10-Jan-2015.)
Assertion
Ref Expression
dfss1 (A B ↔ (BA) = A)

Proof of Theorem dfss1
StepHypRef Expression
1 df-ss 3259 . 2 (A B ↔ (AB) = A)
2 incom 3448 . . 3 (AB) = (BA)
32eqeq1i 2360 . 2 ((AB) = A ↔ (BA) = A)
41, 3bitri 240 1 (A B ↔ (BA) = A)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642   ∩ cin 3208   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  dfss5  3461  sseqin2  3474
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