Theorem sneqi 3681

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 3680	. 2 |- ( A = B -> { A } = { B } )
3	1, 2	ax-mp 5	1 |- { A } = { B }

Syntax hints:   = wceq 1397   {csn 3669

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-sn 3675

This theorem is referenced by:  funopsn  5829  fnressn  5839  fressnfv  5840  snriota  6002  xpassen  7013  ennnfonelem1  13027  strle1g  13188  imasplusg  13390  ghmeqker  13857