Theorem bi2ral 1225

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

Hypothesis

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

Assertion

Ref	Expression
bi2ral	|- (A.x e. A A.y e. B ph <-> A.x e. A A.y e. B ps)

Proof of Theorem bi2ral

Step	Hyp	Ref	Expression
1		biral.1	. . 3 |- (ph <-> ps)
2	1	biral 1223	. 2 |- (A.y e. B ph <-> A.y e. B ps)
3	2	biral 1223	1 |- (A.x e. A A.y e. B ph <-> A.x e. A A.y e. B ps)

Syntax hints:   <-> wb 127  A.wral 1201

This theorem is referenced by:  reu4 1340  fununi 2705  zorn2 3612

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ral 1205

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