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Theorem intsng 3961
 Description: Intersection of a singleton. (Contributed by Stefan O'Rear, 22-Feb-2015.)
Assertion
Ref Expression
intsng (A V{A} = A)

Proof of Theorem intsng
StepHypRef Expression
1 dfsn2 3747 . . 3 {A} = {A, A}
21inteqi 3930 . 2 {A} = {A, A}
3 intprg 3960 . . . 4 ((A V A V) → {A, A} = (AA))
43anidms 626 . . 3 (A V{A, A} = (AA))
5 inidm 3464 . . 3 (AA) = A
64, 5syl6eq 2401 . 2 (A V{A, A} = A)
72, 6syl5eq 2397 1 (A V{A} = A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710   ∩ cin 3208  {csn 3737  {cpr 3738  ∩cint 3926 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-sn 3741  df-pr 3742  df-int 3927 This theorem is referenced by:  intsn  3962
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