Theorem sneqd 2419

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 2417	. 2 |- (A = B -> {A} = {B})
3	1, 2	syl 10	1 |- (ph -> {A} = {B})

Syntax hints:   -> wi 3   = wceq 956  {csn 2409

This theorem is referenced by:  reuunisn 2895  fnressn 3837  tfrlem11 3921  mapsnen 4429  xpassen 4441  xpmapenlem4 4499  0ofval 8447

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-sn 2412

Copyright terms: Public domain