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Theorem inab 3522
 Description: Intersection of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
inab

Proof of Theorem inab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sban 2069 . . 3
2 df-clab 2340 . . 3
3 df-clab 2340 . . . 4
4 df-clab 2340 . . . 4
53, 4anbi12i 678 . . 3
61, 2, 53bitr4ri 269 . 2
76ineqri 3449 1
 Colors of variables: wff setvar class Syntax hints:   wa 358   wceq 1642  wsb 1648   wcel 1710  cab 2339   cin 3208 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 This theorem is referenced by:  inrab  3527  inrab2  3528  dfrab2  3530  dfrab3  3531  evenodddisj  4516  spfinex  4537  pmex  6005  nmembers1lem1  6268
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