Theorem sneqd 1818

Description: Equality deduction for singletons.

Hypothesis

Ref	Expression
sneqd.1	|- (ph -> A = B)

Assertion

Ref	Expression
sneqd	|- (ph -> {A} = {B})

Proof of Theorem sneqd

Step	Hyp	Ref	Expression
1		sneqd.1	. 2 |- (ph -> A = B)
2		sneq 1816	. 2 |- (A = B -> {A} = {B})
3	1, 2	syl 12	1 |- (ph -> {A} = {B})

Syntax hints:   -> wi 2   = wceq 1091  {csn 1808

This theorem is referenced by:  fnressn 2897  tfrlem10 2958  tfrlem11 2959  mapsnen 3334  xpassen 3344  xpmapenlem4 3394

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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