Theorem eqelsuc 3054

Description: A set belongs to the successor of an equal set.

Hypothesis

Ref	Expression
eqelsuc.1	|- A e. V

Assertion

Ref	Expression
eqelsuc	|- (A = B -> A e. suc B)

Proof of Theorem eqelsuc

Step	Hyp	Ref	Expression
1		suceq 3034	. 2 |- (A = B -> suc A = suc B)
2		eqelsuc.1	. . 3 |- A e. V
3	2	sucid 3051	. 2 |- A e. suc A
4	1, 3	syl5eleq 1554	1 |- (A = B -> A e. suc B)

Syntax hints:   -> wi 3   = wceq 956   e. wcel 958  Vcvv 1811  suc csuc 2950

This theorem is referenced by:  tfrlem11 3921  pssnn 4534

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-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-sn 2412  df-pr 2413  df-suc 2954

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