Theorem sneqi 1817

Description: Equality inference for singletons.

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 1816	. 2 ⊢ (A = B → {A} = {B})
3	1, 2	ax-mp 6	1 ⊢ {A} = {B}

Syntax hints:   = wceq 1091  {csn 1808

This theorem is referenced by:  dmsnsnsn 2548  fnressn 2897  fressnfv 2898  df2o2 3112  xpassen 3344  xpmapenlem2 3392  xp2cda 3723

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-sn 1811

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