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Theorem nfra2 3098
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 39630. 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 2916 . 2 𝑦𝐴
2 nfra1 3093 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 3097 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1859  wral 3064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1873  ax-4 1888  ax-5 1994  ax-6 2060  ax-7 2096  ax-9 2157  ax-10 2177  ax-11 2193  ax-12 2206  ax-13 2411  ax-ext 2754
This theorem depends on definitions:  df-bi 198  df-an 384  df-or 864  df-tru 1637  df-ex 1856  df-nf 1861  df-cleq 2767  df-clel 2770  df-nfc 2905  df-ral 3069
This theorem is referenced by:  ralcom2  3256  invdisj  4783  reusv3  5019  dedekind  10423  dedekindle  10424  mreexexd  16536  gsummatr01lem4  20703  ordtconnlem1  30327  bnj1379  31256  tratrb  39284  islptre  40375  sprsymrelfo  42299
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