Theorem eqelsuc 3049

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 3029	. 2 |- (A = B -> suc A = suc B)
2		eqelsuc.1	. . 3 |- A e. V
3	2	sucid 3046	. 2 |- A e. suc A
4	1, 3	syl5eleq 1551	1 |- (A = B -> A e. suc B)

Syntax hints:   -> wi 3   = wceq 954   e. wcel 956  Vcvv 1807  suc csuc 2945

This theorem is referenced by:  tfrlem11 3912  pssnn 4519

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-un 2046  df-sn 2408  df-pr 2409  df-suc 2949

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