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Theorem nfra2 2703
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 28313. 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 2523 . 2  |-  F/_ y A
2 nfra1 2699 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2702 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1550   A.wral 2649
This theorem is referenced by:  ralcom2  2815  invdisj  4142  reusv3  4671  mreexexd  13800  dedekind  24966  dedekindle  24967  tratrb  27963  bnj1379  28540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ral 2654
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