Theorem 19.21bbi 2060

Description: Inference removing double quantifier. Version of 19.21bi 2059 with two quanditiers. (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 2059	. 2 |- ( ph -> A. y ps )
3	2	19.21bi 2059	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   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  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  2mo  2551  pocl  5042  funun  5932  fununi  5964  trclfvcotr  13750  pm14.24  38633