Theorem bj-uniexg 15531

Description: uniexg 4474 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 3848	. . 3 |- ( x = A -> U. x = U. A )
2	1	eleq1d 2265	. 2 |- ( x = A -> ( U. x e. _V <-> U. A e. _V ) )
3		vex 2766	. . 3 |- x e. _V
4	3	bj-uniex 15530	. 2 |- U. x e. _V
5	2, 4	vtoclg 2824	1 |- ( A e. V -> U. A e. _V )

Syntax hints:   -> wi 4   = wceq 1364   e. wcel 2167   _Vcvv 2763   U.cuni 3839

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-13 2169  ax-14 2170  ax-ext 2178  ax-un 4468  ax-bd0 15426  ax-bdex 15432  ax-bdel 15434  ax-bdsb 15435  ax-bdsep 15497

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-v 2765  df-uni 3840  df-bdc 15454

This theorem is referenced by: (None)