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Theorem nfra2 2943
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 38916. Contributed by Alan Sare 31-Dec-2011. (Contributed by NM, 31-Dec-2011.)
Assertion
Ref Expression
nfra2 𝑦𝑥𝐴𝑦𝐵 𝜑
Distinct variable group:   𝑦,𝐴
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥)   𝐵(𝑥,𝑦)

Proof of Theorem nfra2
StepHypRef Expression
1 nfcv 2762 . 2 𝑦𝐴
2 nfra1 2938 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 2942 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1706  wral 2909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ral 2914
This theorem is referenced by:  ralcom2  3099  invdisj  4629  reusv3  4867  dedekind  10185  dedekindle  10186  mreexexd  16289  mreexexdOLD  16290  gsummatr01lem4  20445  ordtconnlem1  29944  bnj1379  30875  tratrb  38566  islptre  39651  sprsymrelfo  41512
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