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Theorem pwssb 4052
 Description: Two ways to express a collection of subclasses. (Contributed by NM, 19-Jul-2006.)
Assertion
Ref Expression
pwssb (A Bx A x B)
Distinct variable groups:   x,A   x,B

Proof of Theorem pwssb
StepHypRef Expression
1 sspwuni 4051 . 2 (A BA B)
2 unissb 3921 . 2 (A Bx A x B)
31, 2bitri 240 1 (A Bx A x B)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wral 2614   ⊆ wss 3257  ℘cpw 3722  ∪cuni 3891 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw 3724  df-uni 3892 This theorem is referenced by: (None)
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