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Theorem nfralwOLD 3308
Description: Obsolete version of nfralw 3307 as of 13-Dec-2024. (Contributed by NM, 1-Sep-1999.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfralw.1 𝑥𝐴
nfralw.2 𝑥𝜑
Assertion
Ref Expression
nfralwOLD 𝑥𝑦𝐴 𝜑
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥,𝑦)

Proof of Theorem nfralwOLD
StepHypRef Expression
1 nftru 1805 . . 3 𝑦
2 nfralw.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfralw.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfraldw 3305 . 2 (⊤ → Ⅎ𝑥𝑦𝐴 𝜑)
76mptru 1547 1 𝑥𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1541  wnf 1784  wnfc 2882  wral 3060
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-10 2136  ax-11 2153  ax-12 2170
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-ex 1781  df-nf 1785  df-clel 2809  df-nfc 2884  df-ral 3061
This theorem is referenced by: (None)
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