Theorem sneqi 3458

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

Step	Hyp	Ref	Expression
1		sneqi.1	. 2 |- A = B
2		sneq 3457	. 2 |- ( A = B -> { A } = { B } )
3	1, 2	ax-mp 7	1 |- { A } = { B }

Syntax hints:   = wceq 1289   {csn 3446

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-sn 3452

This theorem is referenced by:  fnressn  5483  fressnfv  5484  snriota  5637  xpassen  6546  strle1g  11583