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Theorem nfra2 2598
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 27916. 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 2420 . 2  |-  F/_ y A
2 nfra1 2594 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2597 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1531   A.wral 2544
This theorem is referenced by:  ralcom2  2705  invdisj  4013  reusv3  4541  mreexexd  13546  imonclem  25224  ismonc  25225  cmpmon  25226  iepiclem  25234  isepic  25235  stoweidlem60  27220  tratrb  27582
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ral 2549
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