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Theorem nfra2 2775
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 31601. Contributed by Alan Sare 31-Dec-2011. (Contributed by NM, 31-Dec-2011.)
Assertion
Ref Expression
nfra2  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Distinct variable group:    y, A
Allowed substitution hints:    ph( x, y)    A( x)    B( x, y)

Proof of Theorem nfra2
StepHypRef Expression
1 nfcv 2584 . 2  |-  F/_ y A
2 nfra1 2771 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2774 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1589   A.wral 2720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ral 2725
This theorem is referenced by:  ralcom2  2890  invdisj  4286  reusv3  4505  dedekind  9538  dedekindle  9539  mreexexd  14591  gsummatr01lem4  18469  tratrb  31247  bnj1379  31829
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