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Theorem r19.12 2727
 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 2489 . . . 4
2 nfra1 2664 . . . 4
31, 2nfrex 2669 . . 3
4 ax-1 5 . . 3
53, 4ralrimi 2695 . 2
6 rsp 2674 . . . . 5
76com12 27 . . . 4
87reximdv 2725 . . 3
98ralimia 2687 . 2
105, 9syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1710  wral 2614  wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620 This theorem is referenced by:  iuniin  3979
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