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Theorem nfra2 2851
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 32740. 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 2629 . 2  |-  F/_ y A
2 nfra1 2845 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2850 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1599   A.wral 2814
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819
This theorem is referenced by:  ralcom2  3026  invdisj  4436  reusv3  4655  dedekind  9739  dedekindle  9740  mreexexd  14896  gsummatr01lem4  18924  islptre  31161  tratrb  32386  bnj1379  32968
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