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Theorem nfra2 2762
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 29046. 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 2574 . 2  |-  F/_ y A
2 nfra1 2758 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2761 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1554   A.wral 2707
This theorem is referenced by:  ralcom2  2874  invdisj  4204  reusv3  4734  mreexexd  13878  dedekind  25192  dedekindle  25193  tratrb  28694  bnj1379  29276
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712
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