Theorem 3albii 34012

Description: Inference adding three universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 10-Aug-2018.)

Hypothesis

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

Assertion

Ref	Expression
3albii	|- ( A. x A. y A. z ph <-> A. x A. y A. z ps )

Proof of Theorem 3albii

Step	Hyp	Ref	Expression
1		3albii.1	. . 3 |- ( ph <-> ps )
2	1	2albii 1748	. 2 |- ( A. y A. z ph <-> A. y A. z ps )
3	2	albii 1747	1 |- ( A. x A. y A. z ph <-> A. x A. y A. z ps )

Syntax hints:   <-> wb 196   A.wal 1481

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

This theorem is referenced by: (None)