Theorem ralv 2305

Description: A universal quantifier restricted to the universe is unrestricted.

Assertion

Ref	Expression
ralv	|- (A.x e. _V ph <-> A.xph)

Proof of Theorem ralv

Step	Hyp	Ref	Expression
1		df-ral 2109	. 2 |- (A.x e. _V ph <-> A.x(x e. _V -> ph))
2		visset 2295	. . . 4 |- x e. _V
3	2	a1bi 214	. . 3 |- (ph <-> (x e. _V -> ph))
4	3	albii 1346	. 2 |- (A.xph <-> A.x(x e. _V -> ph))
5	1, 4	bitr4i 193	1 |- (A.x e. _V ph <-> A.xph)

Syntax hints:   -> wi 3   <-> wb 163  A.wal 1296   e. wcel 1300  A.wral 2105  _Vcvv 2292

This theorem is referenced by:  ralcom4 2310  ralcom4OLD 2311  viin 3314  ref4w 14370

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-ral 2109  df-v 2294

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