Theorem bj-uniexg 14530

Description: uniexg 4438 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-uniexg	|- ( A e. V -> U. A e. _V )

Proof of Theorem bj-uniexg

Dummy variable x is distinct from all other variables.

Step	Hyp	Ref	Expression
1		unieq 3818	. . 3 |- ( x = A -> U. x = U. A )
2	1	eleq1d 2246	. 2 |- ( x = A -> ( U. x e. _V <-> U. A e. _V ) )
3		vex 2740	. . 3 |- x e. _V
4	3	bj-uniex 14529	. 2 |- U. x e. _V
5	2, 4	vtoclg 2797	1 |- ( A e. V -> U. A e. _V )

Syntax hints:   -> wi 4   = wceq 1353   e. wcel 2148   _Vcvv 2737   U.cuni 3809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-un 4432  ax-bd0 14425  ax-bdex 14431  ax-bdel 14433  ax-bdsb 14434  ax-bdsep 14496

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-uni 3810  df-bdc 14453

This theorem is referenced by: (None)