New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rgen2a Unicode version

Theorem rgen2a 2680
 Description: Generalization rule for restricted quantification. Note that and needn't be distinct (and illustrates the use of dvelim 2016). (Contributed by NM, 23-Nov-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.
Hypothesis
Ref Expression
rgen2a.1
Assertion
Ref Expression
rgen2a
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem rgen2a
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2413 . . . . . . . 8
2 rgen2a.1 . . . . . . . . 9
32ex 423 . . . . . . . 8
41, 3syl6bi 219 . . . . . . 7
54pm2.43d 44 . . . . . 6
65alimi 1559 . . . . 5
76a1d 22 . . . 4
8 eleq1 2413 . . . . . 6
98dvelimv 1939 . . . . 5
103alimi 1559 . . . . 5
119, 10syl6 29 . . . 4
127, 11pm2.61i 156 . . 3
13 df-ral 2619 . . 3
1412, 13sylibr 203 . 2
1514rgen 2679 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349  df-ral 2619 This theorem is referenced by:  vfinnc  4471  ncfinraise  4481  isoid  5490  pw1fnf1o  5855  fce  6188
 Copyright terms: Public domain W3C validator