Theorem sneqi 3634

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 3633	. 2 |- ( A = B -> { A } = { B } )
3	1, 2	ax-mp 5	1 |- { A } = { B }

Syntax hints:   = wceq 1364   {csn 3622

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-sn 3628

This theorem is referenced by:  fnressn  5748  fressnfv  5749  snriota  5907  xpassen  6889  ennnfonelem1  12624  strle1g  12784  imasplusg  12951  ghmeqker  13401