Metamath Proof Explorer


Theorem unisuc

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)

Ref Expression
Hypothesis unisuc.1 𝐴 ∈ V
Assertion unisuc ( Tr 𝐴 suc 𝐴 = 𝐴 )

Proof

Step Hyp Ref Expression
1 unisuc.1 𝐴 ∈ V
2 unisucg ( 𝐴 ∈ V → ( Tr 𝐴 suc 𝐴 = 𝐴 ) )
3 1 2 ax-mp ( Tr 𝐴 suc 𝐴 = 𝐴 )