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Theorem rab0 3418
 Description: Any restricted class abstraction restricted to the empty set is empty. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
rab0

Proof of Theorem rab0
StepHypRef Expression
1 noel 3394 . . . . 5
21intnanr 916 . . . 4
3 equid 1678 . . . . 5
43notnoti 635 . . . 4
52, 42false 691 . . 3
65abbii 2270 . 2
7 df-rab 2441 . 2
8 dfnul2 3392 . 2
96, 7, 83eqtr4i 2185 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 103   wceq 1332   wcel 2125  cab 2140  crab 2436  c0 3390 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rab 2441  df-v 2711  df-dif 3100  df-nul 3391 This theorem is referenced by:  ssfirab  6867  sup00  6935
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