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Theorem nfiotaw 6414
Description: Bound-variable hypothesis builder for the class. Version of nfiota 6416 with a disjoint variable condition, which does not require ax-13 2370. (Contributed by NM, 23-Aug-2011.) (Revised by Gino Giotto, 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 6413 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54mptru 1546 1 𝑥(℩𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wtru 1540  wnf 1783  wnfc 2884  cio 6408
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 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-10 2135  ax-11 2152  ax-12 2169  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 846  df-tru 1542  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2886  df-ral 3062  df-rex 3071  df-v 3439  df-in 3899  df-ss 3909  df-sn 4566  df-uni 4845  df-iota 6410
This theorem is referenced by:  csbiota  6451  nffv  6814  nfsum1  15450  nfsum  15451  nfcprod1  15669  nfcprod  15670  nfafv2  44954
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