Theorem ralimia 2436

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 2435	1 |- ( A. x e. A ph -> A. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 1438   A.wral 2359

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 1381  ax-gen 1383

This theorem depends on definitions:  df-bi 115  df-ral 2364

This theorem is referenced by:  ralimiaa  2437  ralimi  2438  r19.12  2478  rr19.3v  2755  rr19.28v  2756  ffvresb  5461  f1mpt  5550  peano2nnnn  7390  peano5nnnn  7427  peano5nni  8425  peano2nn  8434  serf0  10741