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Theorem nfra2 2668
 Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD in set.mm. Contributed by Alan Sare 31-Dec-2011. (Contributed by NM, 31-Dec-2011.)
Assertion
Ref Expression
nfra2 yx A y B φ
Distinct variable group:   y,A
Allowed substitution hints:   φ(x,y)   A(x)   B(x,y)

Proof of Theorem nfra2
StepHypRef Expression
1 nfcv 2489 . 2 yA
2 nfra1 2664 . 2 yy B φ
31, 2nfral 2667 1 yx A y B φ
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1544  ∀wral 2614 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 This theorem is referenced by:  ralcom2  2775  ncfinraise  4481
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