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Theorem disjne 3422
 Description: Members of disjoint sets are not equal. (Contributed by NM, 28-Mar-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
disjne

Proof of Theorem disjne
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 disj 3417 . . 3
2 eleq1 2203 . . . . . 6
32notbid 657 . . . . 5
43rspccva 2793 . . . 4
5 eleq1a 2212 . . . . 5
65necon3bd 2352 . . . 4
74, 6syl5com 29 . . 3
81, 7sylanb 282 . 2
983impia 1179 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   w3a 963   wceq 1332   wcel 1481   wne 2309  wral 2417   cin 3076  c0 3369 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-ral 2422  df-v 2692  df-dif 3079  df-in 3083  df-nul 3370 This theorem is referenced by: (None)
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