Theorem ralimia 2491

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996.)

Hypothesis

Ref	Expression
ralimia.1	|- ( x e. A -> ( ph -> ps ) )

Assertion

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

Proof of Theorem ralimia

Step	Hyp	Ref	Expression
1		ralimia.1	. . 3 |- ( x e. A -> ( ph -> ps ) )
2	1	a2i 11	. 2 |- ( ( x e. A -> ph ) -> ( x e. A -> ps ) )
3	2	ralimi2 2490	1 |- ( A. x e. A ph -> A. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 1480   A.wral 2414

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425

This theorem depends on definitions:  df-bi 116  df-ral 2419

This theorem is referenced by:  ralimiaa  2492  ralimi  2493  r19.12  2536  rr19.3v  2818  rr19.28v  2819  ffvresb  5576  f1mpt  5665  ixpf  6607  peano2nnnn  7654  peano5nnnn  7693  peano5nni  8716  peano2nn  8725  serf0  11114  baspartn  12206