Theorem 19.21bbi 1547

Description: Inference removing double quantifier. (Contributed by NM, 20-Apr-1994.)

Hypothesis

Ref	Expression
19.21bbi.1	|- ( ph -> A. x A. y ps )

Assertion

Ref	Expression
19.21bbi	|- ( ph -> ps )

Proof of Theorem 19.21bbi

Step	Hyp	Ref	Expression
1		19.21bbi.1	. . 3 |- ( ph -> A. x A. y ps )
2	1	19.21bi 1546	. 2 |- ( ph -> A. y ps )
3	2	19.21bi 1546	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   A.wal 1341

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1498

This theorem is referenced by:  pocl  4281  funun  5232  fununi  5256  imain  5270