Theorem sneqi 3717

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 3716	. 2 ⊢ (𝐴 = 𝐵 → {𝐴} = {𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐴} = {𝐵}

Syntax hints:   = wceq 1402  {csn 3705

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 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 theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-sn 3711

This theorem is referenced by:  funopsn  5882  fnressn  5892  fressnfv  5893  snriota  6060  xpassen  7118  ennnfonelem1  13276  strle1g  13437  imasplusg  13606  ghmeqker  14051