Metamath Proof Explorer


Theorem tskssel

Description: A part of a Tarski class strictly dominated by the class is an element of the class. JFM CLASSES2 th. 2. (Contributed by FL, 22-Feb-2011) (Proof shortened by Mario Carneiro, 20-Sep-2014)

Ref Expression
Assertion tskssel T Tarski A T A T A T

Proof

Step Hyp Ref Expression
1 sdomnen A T ¬ A T
2 1 3ad2ant3 T Tarski A T A T ¬ A T
3 tsken T Tarski A T A T A T
4 3 3adant3 T Tarski A T A T A T A T
5 4 ord T Tarski A T A T ¬ A T A T
6 2 5 mpd T Tarski A T A T A T