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Theorem inss2 3476
 Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of [TakeutiZaring] p. 18. (Contributed by NM, 27-Apr-1994.)
Assertion
Ref Expression
inss2

Proof of Theorem inss2
StepHypRef Expression
1 incom 3448 . 2
2 inss1 3475 . 2
31, 2eqsstr3i 3302 1
 Colors of variables: wff setvar class Syntax hints:   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:  difsscompl  3549  difin0  3623  pw1ss1c  4158  peano5  4409  spfininduct  4540  phialllem2  4617  ssrnres  5059  fnresin2  5198  ffvresb  5431  erdisj  5972  sbthlem1  6203
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