Theorem reubii 2262

Description: Formula-building rule for restricted existential quantifier (inference rule).

Hypothesis

Ref	Expression
reubii.1	|- (ph <-> ps)

Assertion

Ref	Expression
reubii	|- (E!x e. A ph <-> E!x e. A ps)

Proof of Theorem reubii

Step	Hyp	Ref	Expression
1		reubii.1	. . 3 |- (ph <-> ps)
2	1	a1i 8	. 2 |- (x e. A -> (ph <-> ps))
3	2	reubiia 2261	1 |- (E!x e. A ph <-> E!x e. A ps)

Syntax hints:   <-> wb 163   e. wcel 1300  E!wreu 2107

This theorem is referenced by:  aceq2 5893  infmsup 7277  uzwo3 7431  cnlnadjlem3 11639  cnlnadjlem4 11640  cnlnadjlem5 11641

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

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-eu 1775  df-reu 2111

Copyright terms: Public domain