Theorem 3ralbii 34013

Description: Inference adding three restricted universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 25-Jul-2019.)

Hypothesis

Ref	Expression
3ralbii.1	|- ( ph <-> ps )

Assertion

Ref	Expression
3ralbii	|- ( A. x e. A A. y e. B A. z e. C ph <-> A. x e. A A. y e. B A. z e. C ps )

Proof of Theorem 3ralbii

Step	Hyp	Ref	Expression
1		3ralbii.1	. . 3 |- ( ph <-> ps )
2	1	2ralbii 2981	. 2 |- ( A. y e. B A. z e. C ph <-> A. y e. B A. z e. C ps )
3	2	ralbii 2980	1 |- ( A. x e. A A. y e. B A. z e. C ph <-> A. x e. A A. y e. B A. z e. C ps )

Syntax hints:   <-> wb 196   A.wral 2912

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ral 2917

This theorem is referenced by: (None)