Theorem wunsuc

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

	Ref	Expression
Hypotheses	wununi.1	|- ( ph -> U e. WUni )
	wununi.2	|- ( ph -> A e. U )
Assertion	wunsuc	|- ( ph -> suc A e. U )

Proof

Step	Hyp	Ref	Expression
1		wununi.1	|- ( ph -> U e. WUni )
2		wununi.2	|- ( ph -> A e. U )
3		df-suc	|- suc A = ( A u. { A } )
4	1 2	wunsn	|- ( ph -> { A } e. U )
5	1 2 4	wunun	|- ( ph -> ( A u. { A } ) e. U )
6	3 5	eqeltrid	|- ( ph -> suc A e. U )