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Theorem nfiotaw 6518
Description: Bound-variable hypothesis builder for the class. Version of nfiota 6520 with a disjoint variable condition, which does not require ax-13 2377. (Contributed by NM, 23-Aug-2011.) Avoid ax-13 2377. (Revised by GG, 26-Jan-2024.)
Hypothesis
Ref Expression
nfiotaw.1 𝑥𝜑
Assertion
Ref Expression
nfiotaw 𝑥(℩𝑦𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfiotaw
StepHypRef Expression
1 nftru 1804 . . 3 𝑦
2 nfiotaw.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotadw 6517 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54mptru 1547 1 𝑥(℩𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1541  wnf 1783  wnfc 2890  cio 6512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-rex 3071  df-v 3482  df-ss 3968  df-sn 4627  df-uni 4908  df-iota 6514
This theorem is referenced by:  csbiota  6554  nffv  6916  nfsum1  15726  nfsum  15727  nfcprod1  15944  nfcprod  15945  nfafv2  47230
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