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Theorem sneqd 3746
 Description: Equality deduction for singletons. (Contributed by NM, 22-Jan-2004.)
Hypothesis
Ref Expression
sneqd.1 (φA = B)
Assertion
Ref Expression
sneqd (φ → {A} = {B})

Proof of Theorem sneqd
StepHypRef Expression
1 sneqd.1 . 2 (φA = B)
2 sneq 3744 . 2 (A = B → {A} = {B})
31, 2syl 15 1 (φ → {A} = {B})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  {csn 3737 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-sn 3741 This theorem is referenced by:  elp6  4263  pw1eqadj  4332  elimapw13  4946  dmsnopg  5066  fnunsn  5190  fsng  5433  fnressn  5438  fvsng  5446  freceq12  6311
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