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Theorem nfrmowOLD 3397
Description: Obsolete version of nfrmow 3385 as of 21-Nov-2024. (Contributed by NM, 16-Jun-2017.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfreuwOLD.1 𝑥𝐴
nfreuwOLD.2 𝑥𝜑
Assertion
Ref Expression
nfrmowOLD 𝑥∃*𝑦𝐴 𝜑
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥,𝑦)

Proof of Theorem nfrmowOLD
StepHypRef Expression
1 df-rmo 3352 . 2 (∃*𝑦𝐴 𝜑 ↔ ∃*𝑦(𝑦𝐴𝜑))
2 nftru 1807 . . . 4 𝑦
3 nfcvd 2907 . . . . . 6 (⊤ → 𝑥𝑦)
4 nfreuwOLD.1 . . . . . . 7 𝑥𝐴
54a1i 11 . . . . . 6 (⊤ → 𝑥𝐴)
63, 5nfeld 2917 . . . . 5 (⊤ → Ⅎ𝑥 𝑦𝐴)
7 nfreuwOLD.2 . . . . . 6 𝑥𝜑
87a1i 11 . . . . 5 (⊤ → Ⅎ𝑥𝜑)
96, 8nfand 1901 . . . 4 (⊤ → Ⅎ𝑥(𝑦𝐴𝜑))
102, 9nfmodv 2559 . . 3 (⊤ → Ⅎ𝑥∃*𝑦(𝑦𝐴𝜑))
1110mptru 1549 . 2 𝑥∃*𝑦(𝑦𝐴𝜑)
121, 11nfxfr 1856 1 𝑥∃*𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 397  wtru 1543  wnf 1786  wcel 2107  ∃*wmo 2538  wnfc 2886  ∃*wrmo 3351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-mo 2540  df-cleq 2730  df-clel 2816  df-nfc 2888  df-rmo 3352
This theorem is referenced by: (None)
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