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Theorem nfra2 2930
 Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 38118. 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 2751 . 2 𝑦𝐴
2 nfra1 2925 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 2929 1 𝑦𝑥𝐴𝑦𝐵 𝜑
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1699  ∀wral 2896 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901 This theorem is referenced by:  ralcom2  3083  invdisj  4571  reusv3  4802  dedekind  10079  dedekindle  10080  mreexexd  16131  mreexexdOLD  16132  gsummatr01lem4  20283  ordtconlem1  29298  bnj1379  30155  tratrb  37767  islptre  38686
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