Mathbox for Frédéric Liné < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  r19.2zr Unicode version

Theorem r19.2zr 25060
 Description: Quantifying a hypothesis with a universal restricted quantifier. (Contributed by FL, 19-Sep-2011.)
Hypothesis
Ref Expression
r19.2zr.1
Assertion
Ref Expression
r19.2zr
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem r19.2zr
StepHypRef Expression
1 r19.2z 3556 . 2
2 r19.2zr.1 . . 3
32rexlimivw 2676 . 2
41, 3syl 15 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wne 2459  wral 2556  wrex 2557  c0 3468 This theorem is referenced by:  r19.2zrr  25061 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-nul 3469
 Copyright terms: Public domain W3C validator