MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfra2 Structured version   Visualization version   GIF version

Theorem nfra2 3369
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 44299. Usage of this theorem is discouraged because it depends on ax-13 2367. Use the weaker nfra2w 3293 when possible. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.)
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 2899 . 2 𝑦𝐴
2 nfra1 3278 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 3367 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1778  wral 3058
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-13 2367  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ral 3059
This theorem is referenced by:  ralcom2  3370
  Copyright terms: Public domain W3C validator