Theorem 19.21bbi 1063

Description: Inference removing double quantifier.

Hypothesis

Ref	Expression
19.21bbi.1	|- (ph -> A.xA.yps)

Assertion

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

Proof of Theorem 19.21bbi

Step	Hyp	Ref	Expression
1		19.21bbi.1	. . 3 |- (ph -> A.xA.yps)
2	1	19.21bi 1062	. 2 |- (ph -> A.yps)
3	2	19.21bi 1062	1 |- (ph -> ps)

Syntax hints:   -> wi 3  A.wal 956

This theorem is referenced by:  trel 2692  pocl 2850  funun 3560  fillsb 10546  cmpmon 10714

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-4 975

Copyright terms: Public domain