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Theorem nfra2 2812
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 37117. 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 2584 . 2  |-  F/_ y A
2 nfra1 2806 . 2  |-  F/ y A. y  e.  B  ph
31, 2nfral 2811 1  |-  F/ y A. x  e.  A  A. y  e.  B  ph
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1663   A.wral 2775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780
This theorem is referenced by:  ralcom2  2993  invdisj  4409  reusv3  4628  dedekind  9797  dedekindle  9798  mreexexd  15541  gsummatr01lem4  19669  ordtconlem1  28725  bnj1379  29637  tratrb  36754  islptre  37518
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