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Theorem nfra2 2599
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 28709. 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 2421 . 2  |-  F/_ y A
2 nfra1 2595 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2598 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1533   A.wral 2545
This theorem is referenced by:  ralcom2  2706  invdisj  4014  reusv3  4544  mreexexd  13552  imonclem  25824  ismonc  25825  cmpmon  25826  iepiclem  25834  isepic  25835  stoweidlem60  27820  tratrb  28355
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ral 2550
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