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Theorem nfra2 2673
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 28381. 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 2494 . 2  |-  F/_ y A
2 nfra1 2669 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2672 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1544   A.wral 2619
This theorem is referenced by:  ralcom2  2780  invdisj  4091  reusv3  4621  mreexexd  13643  stoweidlem60  27132  tratrb  28027
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 1930  ax-ext 2339
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 2351  df-clel 2354  df-nfc 2483  df-ral 2624
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