Theorem uniexd 4441

Description: Deduction version of the ZF Axiom of Union in class notation. (Contributed by Glauco Siliprandi, 26-Jun-2021.)

Hypothesis

Ref	Expression
uniexd.1	|- ( ph -> A e. V )

Assertion

Ref	Expression
uniexd	|- ( ph -> U. A e. _V )

Proof of Theorem uniexd

Step	Hyp	Ref	Expression
1		uniexd.1	. 2 |- ( ph -> A e. V )
2		uniexg 4440	. 2 |- ( A e. V -> U. A e. _V )
3	1, 2	syl 14	1 |- ( ph -> U. A e. _V )

Syntax hints:   -> wi 4   e. wcel 2148   _Vcvv 2738   U.cuni 3810

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-sep 4122  ax-un 4434

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 2740  df-uni 3811

This theorem is referenced by:  supex2g  7032  ptex  12713