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Theorem iin0imm 3949
Description: An indexed intersection of the empty set, with an inhabited index set, is empty. (Contributed by Jim Kingdon, 29-Aug-2018.)
Assertion
Ref Expression
iin0imm (∃𝑦 𝑦𝐴 𝑥𝐴 ∅ = ∅)
Distinct variable groups:   𝑦,𝐴   𝑥,𝐴

Proof of Theorem iin0imm
StepHypRef Expression
1 iinconstm 3694 1 (∃𝑦 𝑦𝐴 𝑥𝐴 ∅ = ∅)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1259  wex 1397  wcel 1409  c0 3252   ciin 3686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-iin 3688
This theorem is referenced by: (None)
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