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Theorem ssind 3479
 Description: A deduction showing that a subclass of two classes is a subclass of their intersection. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
ssind.1
ssind.2
Assertion
Ref Expression
ssind

Proof of Theorem ssind
StepHypRef Expression
1 ssind.1 . 2
2 ssind.2 . 2
3 ssin 3477 . . 3
43biimpi 186 . 2
51, 2, 4syl2anc 642 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   cin 3208   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-ss 3259 This theorem is referenced by: (None)
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