Theorem ralimia 2605

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 2604	1 |- ( A. x e. A ph -> A. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 2205   A.wral 2522

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 1496  ax-gen 1498

This theorem depends on definitions:  df-bi 117  df-ral 2527

This theorem is referenced by:  ralimiaa  2606  ralimi  2607  r19.12  2651  rr19.3v  2958  rr19.28v  2959  ffvresb  5842  f1mpt  5946  ixpf  6957  exmidontri2or  7555  peano2nnnn  8170  peano5nnnn  8209  peano5nni  9242  peano2nn  9251  serf0  12041  baspartn  14932  tridceq  16858