Theorem exlimd 1806

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
exlimd.1	|- F/xph
exlimd.2	|- F/xch
exlimd.3	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
exlimd	|- (ph -> (E.xps -> ch))

Proof of Theorem exlimd

Step	Hyp	Ref	Expression
1		exlimd.1	. . 3 |- F/xph
2		exlimd.3	. . 3 |- (ph -> (ps -> ch))
3	1, 2	alrimi 1765	. 2 |- (ph -> A.x(ps -> ch))
4		exlimd.2	. . 3 |- F/xch
5	4	19.23 1801	. 2 |- (A.x(ps -> ch) <-> (E.xps -> ch))
6	3, 5	sylib 188	1 |- (ph -> (E.xps -> ch))

Syntax hints:   -> wi 4  A.wal 1540  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  exlimdh  1807  exlimdd  1889  equs5  1996  exists2  2294  ceqsalg  2884  copsex2t  4609  mosubopt  4613  ov3  5600