Theorem hbeud 1970

Description: Deduction version of hbeu 1969. (Contributed by NM, 15-Feb-2013.) (Proof rewritten by Jim Kingdon, 25-May-2018.)

Hypotheses

Ref	Expression
hbeud.1	|- ( ph -> A. x ph )
hbeud.2	|- ( ph -> A. y ph )
hbeud.3	|- ( ph -> ( ps -> A. x ps ) )

Assertion

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

Proof of Theorem hbeud

Step	Hyp	Ref	Expression
1		hbeud.2	. . . 4 |- ( ph -> A. y ph )
2	1	nfi 1396	. . 3 |- F/ y ph
3		hbeud.1	. . . . 5 |- ( ph -> A. x ph )
4	3	nfi 1396	. . . 4 |- F/ x ph
5		hbeud.3	. . . 4 |- ( ph -> ( ps -> A. x ps ) )
6	4, 5	nfd 1461	. . 3 |- ( ph -> F/ x ps )
7	2, 6	nfeud 1964	. 2 |- ( ph -> F/ x E! y ps )
8	7	nfrd 1458	1 |- ( ph -> ( E! y ps -> A. x E! y ps ) )

Syntax hints:   -> wi 4   A.wal 1287   E!weu 1948

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951

This theorem is referenced by: (None)