Theorem sneqi 3387

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 3386	. 2 |- ( A = B -> { A } = { B } )
3	1, 2	ax-mp 7	1 |- { A } = { B }

Syntax hints:   = wceq 1243   {csn 3375

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-sn 3381

This theorem is referenced by:  fnressn  5349  fressnfv  5350  snriota  5497  xpassen  6304