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Theorem sneqi 3745
Description: Equality inference for singletons. (Contributed by NM, 22-Jan-2004.)
Hypothesis
Ref Expression
sneqi.1 A = B
Assertion
Ref Expression
sneqi {A} = {B}

Proof of Theorem sneqi
StepHypRef Expression
1 sneqi.1 . 2 A = B
2 sneq 3744 . 2 (A = B → {A} = {B})
31, 2ax-mp 5 1 {A} = {B}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1642  {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-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:  pw1eqadj  4332  fnressn  5438  fressnfv  5439
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