Theorem sneqi 3721

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 3720	. 2 |- ( A = B -> { A } = { B } )
3	1, 2	ax-mp 5	1 |- { A } = { B }

This proof depends on syntax axioms:   = wceq 1402   {csn 3709

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-sn 3715

This theorem is used by:  funopsn  5891  fnressn  5901  fressnfv  5902  snriota  6070  xpassen  7128  ennnfonelem1  13298  strle1g  13460  imasplusg  13629  ghmeqker  14074