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Theorem ineq12i 3136
 Description: Equality inference for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
ineq1i.1
ineq12i.2
Assertion
Ref Expression
ineq12i

Proof of Theorem ineq12i
StepHypRef Expression
1 ineq1i.1 . 2
2 ineq12i.2 . 2
3 ineq12 3133 . 2
41, 2, 3mp2an 402 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   cin 2916 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924 This theorem is referenced by:  undir  3187  difindir  3192  inrab  3209  inrab2  3210  inxp  4470  resindi  4627  resindir  4628  cnvin  4731  rnin  4733  inimass  4740  funtp  4952  imainlem  4980  imain  4981  offres  5762  enq0enq  6529
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