Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elin2d Unicode version

Theorem elin2d 3266
 Description: Elementhood in the first set of an intersection - deduction version. (Contributed by Thierry Arnoux, 3-May-2020.)
Hypothesis
Ref Expression
elin1d.1
Assertion
Ref Expression
elin2d

Proof of Theorem elin2d
StepHypRef Expression
1 elin1d.1 . 2
2 elinel2 3263 . 2
31, 2syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1480   cin 3070 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077 This theorem is referenced by:  elfi2  6860  fiuni  6866  fifo  6868  explecnv  11286  restbasg  12351  txcnp  12454  blin2  12615
 Copyright terms: Public domain W3C validator