Theorem ral2imi 2427

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 2426	. 2 |- ( A. x e. A ph -> A. x e. A ( ps -> ch ) )
3		ralim 2422	. 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 2348

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-5 1376  ax-gen 1378

This theorem depends on definitions:  df-bi 115  df-ral 2353

This theorem is referenced by:  r19.26  2485  iinerm  6201  bj-findis  10774