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Theorem ssind 3306
 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 3304 . . 3
43biimpi 119 . 2
51, 2, 4syl2anc 409 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   cin 3076   wss 3077 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 2692  df-in 3083  df-ss 3090 This theorem is referenced by:  ntrin  12366  lmss  12488
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