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Theorem r19.12 2416
Description: Theorem 19.12 of [Margaris] p. 89 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.12
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem r19.12
StepHypRef Expression
1 nfcv 2175 . . . 4  F/_
2 nfra1 2349 . . . 4  F/
31, 2nfrexxy 2355 . . 3  F/
4 ax-1 5 . . 3
53, 4ralrimi 2384 . 2
6 rsp 2363 . . . . 5
76com12 27 . . . 4
87reximdv 2414 . . 3
98ralimia 2376 . 2
105, 9syl 14 1
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390  wral 2300  wrex 2301
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306
This theorem is referenced by:  iuniin  3658
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