Metamath Proof Explorer


Theorem wunres

Description: A weak universe is closed under restrictions. (Contributed by Mario Carneiro, 12-Jan-2017)

Ref Expression
Hypotheses wun0.1 φ U WUni
wunop.2 φ A U
Assertion wunres φ A B U

Proof

Step Hyp Ref Expression
1 wun0.1 φ U WUni
2 wunop.2 φ A U
3 resss A B A
4 3 a1i φ A B A
5 1 2 4 wunss φ A B U