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Theorem eldifsni 3840
 Description: Membership in a set with an element removed. (Contributed by NM, 10-Mar-2015.)
Assertion
Ref Expression
eldifsni (A (B {C}) → AC)

Proof of Theorem eldifsni
StepHypRef Expression
1 eldifsn 3839 . 2 (A (B {C}) ↔ (A B AC))
21simprbi 450 1 (A (B {C}) → AC)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710   ≠ wne 2516   ∖ cdif 3206  {csn 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-sn 3741 This theorem is referenced by:  neldifsn  3841
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