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Theorem nfra2 3222
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 41490. Usage of this theorem is discouraged because it depends on ax-13 2392. Use the weaker nfra2w 3221 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 2982 . 2 𝑦𝐴
2 nfra1 3213 . 2 𝑦𝑦𝐵 𝜑
31, 2nfral 3220 1 𝑦𝑥𝐴𝑦𝐵 𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1785  wral 3133
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-13 2392  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138
This theorem is referenced by:  ralcom2  3354
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