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Theorem unisuc 6465
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 6464 . 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 1537  wcel 2106  Vcvv 3478   cuni 4912  Tr wtr 5265  suc csuc 6388
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980  df-sn 4632  df-pr 4634  df-uni 4913  df-tr 5266  df-suc 6392
This theorem is referenced by:  ordunisuc  7852
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