Theorem 2ralbii 1716

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 1714	. 2 |- (A.y e. B ph <-> A.y e. B ps)
3	2	ralbii 1714	1 |- (A.x e. A A.y e. B ph <-> A.x e. A A.y e. B ps)

Syntax hints:   <-> wb 153  A.wral 1692

This theorem is referenced by:  cnvso 3580  fununi 3620  zorn 4859  isbasis2g 7701  dfadj2 9895  adjval2 9898  cnlnadjeui 10093  adjbdln 10099

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-4 1014  ax-5o 1016

This theorem depends on definitions:  df-bi 154  df-an 232  df-ral 1696

Copyright terms: Public domain