Theorem ral2imi 2552

Description: Inference quantifying antecedent, nested antecedent, and consequent, with a strong hypothesis. (Contributed by NM, 19-Dec-2006.)

Hypothesis

Ref	Expression
ral2imi.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
ral2imi	|- ( A. x e. A ph -> ( A. x e. A ps -> A. x e. A ch ) )

Proof of Theorem ral2imi

Step	Hyp	Ref	Expression
1		ral2imi.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	ralimi 2550	. 2 |- ( A. x e. A ph -> A. x e. A ( ps -> ch ) )
3		ralim 2546	. 2 |- ( A. x e. A ( ps -> ch ) -> ( A. x e. A ps -> A. x e. A ch ) )
4	2, 3	syl 14	1 |- ( A. x e. A ph -> ( A. x e. A ps -> A. x e. A ch ) )

Syntax hints:   -> wi 4   A.wral 2465

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 1457  ax-gen 1459

This theorem depends on definitions:  df-bi 117  df-ral 2470

This theorem is referenced by:  r19.26  2613  r19.30dc  2634  iinerm  6621  ss2ixp  6725  bj-findis  15027