Theorem sneqd 2423

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 2421	. 2 |- (A = B -> {A} = {B})
3	1, 2	syl 10	1 |- (ph -> {A} = {B})

Syntax hints:   -> wi 3   = wceq 958  {csn 2413

This theorem is referenced by:  reuunisn 2901  fnressn 3843  tfrlem11 3927  mapsnen 4435  xpassen 4447  xpmapenlem4 4505  0ofval 8443

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-sn 2416

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