Metamath Proof Explorer


Theorem nfiung

Description: Bound-variable hypothesis builder for indexed union. Usage of this theorem is discouraged because it depends on ax-13 . See nfiun for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by Mario Carneiro, 25-Jan-2014) (New usage is discouraged.)

Ref Expression
Hypotheses nfiung.1 _yA
nfiung.2 _yB
Assertion nfiung _yxAB

Proof

Step Hyp Ref Expression
1 nfiung.1 _yA
2 nfiung.2 _yB
3 df-iun xAB=z|xAzB
4 2 nfcri yzB
5 1 4 nfrex yxAzB
6 5 nfabg _yz|xAzB
7 3 6 nfcxfr _yxAB