Theorem sneqi 3745

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 3744	. 2 ⊢ (A = B → {A} = {B})
3	1, 2	ax-mp 5	1 ⊢ {A} = {B}

Syntax hints:   = wceq 1642  {csn 3737

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-sn 3741

This theorem is referenced by:  pw1eqadj  4332  fnressn  5438  fressnfv  5439