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Theorem unssi 3438
 Description: An inference showing the union of two subclasses is a subclass. (Contributed by Raph Levien, 10-Dec-2002.)
Hypotheses
Ref Expression
unssi.1 A C
unssi.2 B C
Assertion
Ref Expression
unssi (AB) C

Proof of Theorem unssi
StepHypRef Expression
1 unssi.1 . . 3 A C
2 unssi.2 . . 3 B C
31, 2pm3.2i 441 . 2 (A C B C)
4 unss 3437 . 2 ((A C B C) ↔ (AB) C)
53, 4mpbi 199 1 (AB) C
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   ∪ cun 3207   ⊆ wss 3257 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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259 This theorem is referenced by: (None)
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