Theorem wuntr

Description: A weak universe is transitive. (Contributed by Mario Carneiro, 2-Jan-2017)

	Ref	Expression
Assertion	wuntr	|- ( U e. WUni -> Tr U )

Proof

Step	Hyp	Ref	Expression
1		iswun	|- ( U e. WUni -> ( U e. WUni <-> ( Tr U /\ U =/= (/) /\ A. x e. U ( U. x e. U /\ ~P x e. U /\ A. y e. U { x , y } e. U ) ) ) )
2	1	ibi	|- ( U e. WUni -> ( Tr U /\ U =/= (/) /\ A. x e. U ( U. x e. U /\ ~P x e. U /\ A. y e. U { x , y } e. U ) ) )
3	2	simp1d	|- ( U e. WUni -> Tr U )