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Theorem ssind 3155
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  C_
ssind.2  C_  C
Assertion
Ref Expression
ssind  C_  i^i  C

Proof of Theorem ssind
StepHypRef Expression
1 ssind.1 . 2  C_
2 ssind.2 . 2  C_  C
3 ssin 3153 . . 3  C_  C_  C  C_  i^i  C
43biimpi 113 . 2  C_  C_  C  C_  i^i  C
51, 2, 4syl2anc 391 1  C_  i^i  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97    i^i cin 2910    C_ wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
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