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Theorem ssiin 4016
 Description: Subset theorem for an indexed intersection. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
ssiin (C x A Bx A C B)
Distinct variable group:   x,C
Allowed substitution hints:   A(x)   B(x)

Proof of Theorem ssiin
StepHypRef Expression
1 nfcv 2489 . 2 xC
21ssiinf 4015 1 (C x A Bx A C B)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wral 2614   ⊆ wss 3257  ∩ciin 3970 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-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-iin 3972 This theorem is referenced by: (None)
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