Theorem hbexd 1694

Description: Deduction form of bound-variable hypothesis builder hbex 1636. (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 1611	. 2 |- ( ph -> ( E. y ps -> E. y A. x ps ) )
4		19.12 1665	. 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 1351   E.wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)