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