Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ralimdaa Unicode version

Theorem ralimdaa 2859
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-Sep-2003.) (Proof shortened by Wolf Lammen, 29-Dec-2019.)
Hypotheses
Ref Expression
ralimdaa.1
ralimdaa.2
Assertion
Ref Expression
ralimdaa

Proof of Theorem ralimdaa
StepHypRef Expression
1 ralimdaa.1 . . 3
2 ralimdaa.2 . . . 4
32ex 434 . . 3
41, 3ralrimi 2857 . 2
5 ralim 2846 . 2
64, 5syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  A.wral 2807 This theorem is referenced by:  ralimdvaOLD  2866  eltsk2g  9150  ptcnplem  20122  infrglb  31584  stoweidlem61  31843  stoweid  31845  fourierdlem73  31962 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812
 Copyright terms: Public domain W3C validator