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

Theorem r19.2zrr 25061
Description: Removing a universal restricted quantifier when the variable doesn't occur in the proposition. (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
r19.2zrr  |-  ( ( A  =/=  (/)  /\  A. x  e.  A  ph )  ->  ph )
Distinct variable groups:    x, A    ph, x

Proof of Theorem r19.2zrr
StepHypRef Expression
1 id 19 . 2  |-  ( ph  ->  ph )
21r19.2zr 25060 1  |-  ( ( A  =/=  (/)  /\  A. x  e.  A  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    =/= wne 2459   A.wral 2556   (/)c0 3468
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