Theorem hbexd 1687

Description: Deduction form of bound-variable hypothesis builder hbex 1629. (Contributed by NM, 2-Jan-2002.)

Hypotheses

Ref	Expression
hbexd.1	|- ( ph -> A. y ph )
hbexd.2	|- ( ph -> ( ps -> A. x ps ) )

Assertion

Ref	Expression
hbexd	|- ( ph -> ( E. y ps -> A. x E. y ps ) )

Proof of Theorem hbexd

Step	Hyp	Ref	Expression
1		hbexd.1	. . 3 |- ( ph -> A. y ph )
2		hbexd.2	. . 3 |- ( ph -> ( ps -> A. x ps ) )
3	1, 2	eximdh 1604	. 2 |- ( ph -> ( E. y ps -> E. y A. x ps ) )
4		19.12 1658	. 2 |- ( E. y A. x ps -> A. x E. y ps )
5	3, 4	syl6 33	1 |- ( ph -> ( E. y ps -> A. x E. y ps ) )

Syntax hints:   -> wi 4   A.wal 1346   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)