Theorem 2ralbii 1661

Description: Inference adding 2 restricted universal quantifiers to both sides of an equivalence.

Hypothesis

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

Assertion

Ref	Expression
2ralbii	|- (A.x e. A A.y e. B ph <-> A.x e. A A.y e. B ps)

Proof of Theorem 2ralbii

Step	Hyp	Ref	Expression
1		ralbii.1	. . 3 |- (ph <-> ps)
2	1	ralbii 1659	. 2 |- (A.y e. B ph <-> A.y e. B ps)
3	2	ralbii 1659	1 |- (A.x e. A A.y e. B ph <-> A.x e. A A.y e. B ps)

Syntax hints:   <-> wb 146  A.wral 1637

This theorem is referenced by:  cnvso 3509  fununi 3549  zorn 4769  isbasis2g 7554  dfadj2 9729  adjval2t 9732  cnlnadjeu 9925  adjbdlnt 9931

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

This theorem depends on definitions:  df-bi 147  df-an 225  df-ral 1641

Copyright terms: Public domain