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Theorem raleqbi1dv 2507
Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 16-Nov-1995.)
Hypothesis
Ref Expression
raleqd.1
Assertion
Ref Expression
raleqbi1dv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem raleqbi1dv
StepHypRef Expression
1 raleq 2499 . 2
2 raleqd.1 . . 3
32ralbidv 2320 . 2
41, 3bitrd 177 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  peano5  4264  isoeq4  5387  pitonn  6744  peano5nni  7698  1nn  7706  peano2nn  7707  dfuzi  8124  bj-indeq  9386  bj-nntrans  9409
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