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Theorem nfra2 2975
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 39410. 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 2793 . 2 𝑦𝐴
2 nfra1 2970 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 2974 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1748  wral 2941
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946
This theorem is referenced by:  ralcom2  3133  invdisj  4670  reusv3  4906  dedekind  10238  dedekindle  10239  mreexexd  16355  mreexexdOLD  16356  gsummatr01lem4  20512  ordtconnlem1  30098  bnj1379  31027  tratrb  39063  islptre  40169  sprsymrelfo  42072
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