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Theorem unisuc 6462
Description: A transitive class is equal to the union of its successor, inference form. Combines Theorem 4E of [Enderton] p. 72 and Exercise 6 of [Enderton] p. 73. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unisuc.1 𝐴 ∈ V
Assertion
Ref Expression
unisuc (Tr 𝐴 suc 𝐴 = 𝐴)

Proof of Theorem unisuc
StepHypRef Expression
1 unisuc.1 . 2 𝐴 ∈ V
2 unisucg 6461 . 2 (𝐴 ∈ V → (Tr 𝐴 suc 𝐴 = 𝐴))
31, 2ax-mp 5 1 (Tr 𝐴 suc 𝐴 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1539  wcel 2107  Vcvv 3479   cuni 4906  Tr wtr 5258  suc csuc 6385
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-un 3955  df-ss 3967  df-sn 4626  df-pr 4628  df-uni 4907  df-tr 5259  df-suc 6389
This theorem is referenced by:  ordunisuc  7853
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