Theorem ralrimd 2703

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 16-Feb-2004.)

Hypotheses

Ref	Expression
ralrimd.1	|- F/xph
ralrimd.2	|- F/xps
ralrimd.3	|- (ph -> (ps -> (x e. A -> ch)))

Assertion

Ref	Expression
ralrimd	|- (ph -> (ps -> A.x e. A ch))

Proof of Theorem ralrimd

Step	Hyp	Ref	Expression
1		ralrimd.1	. . 3 |- F/xph
2		ralrimd.2	. . 3 |- F/xps
3		ralrimd.3	. . 3 |- (ph -> (ps -> (x e. A -> ch)))
4	1, 2, 3	alrimd 1769	. 2 |- (ph -> (ps -> A.x(x e. A -> ch)))
5		df-ral 2620	. 2 |- (A.x e. A ch <-> A.x(x e. A -> ch))
6	4, 5	syl6ibr 218	1 |- (ph -> (ps -> A.x e. A ch))

Syntax hints:   -> wi 4  A.wal 1540   F/wnf 1544   e. wcel 1710  A.wral 2615

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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2620

This theorem is referenced by:  ralrimdv  2704  ncfinraise  4482