Theorem bnj1469 13146

Description: First-order logic and set theory.

Hypothesis

Ref	Expression
bnj1469.1	|- (ph -> A e. _V)

Assertion

Ref	Expression
bnj1469	|- (ph -> U.A e. _V)

Proof of Theorem bnj1469

Step	Hyp	Ref	Expression
1		bnj1469.1	. 2 |- (ph -> A e. _V)
2		uniexg 3795	. 2 |- (A e. _V -> U.A e. _V)
3	1, 2	syl 12	1 |- (ph -> U.A e. _V)

Syntax hints:   -> wi 3   e. wcel 1300  _Vcvv 2292  U.cuni 3177

This theorem is referenced by:  bnj1489 13554

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-13 1311  ax-14 1312  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865  ax-sep 3438  ax-un 3790

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-rex 2110  df-v 2294  df-uni 3178

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