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Theorem fint 5245
 Description: Function into an intersection. (The proof was shortened by Andrew Salmon, 17-Sep-2011.) (Contributed by set.mm contributors, 14-Oct-1999.) (Revised by set.mm contributors, 18-Sep-2011.)
Hypothesis
Ref Expression
fint.1
Assertion
Ref Expression
fint
Distinct variable groups:   ,   ,   ,

Proof of Theorem fint
StepHypRef Expression
1 ssint 3942 . . . 4
21anbi2i 675 . . 3
3 fint.1 . . . 4
4 r19.28zv 3645 . . . 4
53, 4ax-mp 5 . . 3
62, 5bitr4i 243 . 2
7 df-f 4791 . 2
8 df-f 4791 . . 3
98ralbii 2638 . 2
106, 7, 93bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358   wne 2516  wral 2614   wss 3257  c0 3550  cint 3926   crn 4773   wfn 4776  wf 4777 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551  df-int 3927  df-f 4791 This theorem is referenced by: (None)
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