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Mirrors > Home > MPE Home > Th. List > nfriota | Structured version Visualization version GIF version |
Description: A variable not free in a wff remains so in a restricted iota descriptor. (Contributed by NM, 12-Oct-2011.) |
Ref | Expression |
---|---|
nfriota.1 | ⊢ Ⅎ𝑥𝜑 |
nfriota.2 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfriota | ⊢ Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1721 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfriota.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | nfriota.2 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
5 | 4 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
6 | 1, 3, 5 | nfriotad 6519 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑)) |
7 | 6 | trud 1484 | 1 ⊢ Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1476 Ⅎwnf 1699 Ⅎwnfc 2738 ℩crio 6510 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-sn 4126 df-uni 4373 df-iota 5768 df-riota 6511 |
This theorem is referenced by: csbriota 6523 nfoi 8302 lble 10854 riotasvd 33260 riotasv2d 33261 riotasv2s 33262 cdleme26ee 34666 cdleme31sn1 34687 cdlemefs32sn1aw 34720 cdleme43fsv1snlem 34726 cdleme41sn3a 34739 cdleme32d 34750 cdleme32f 34752 cdleme40m 34773 cdleme40n 34774 cdlemk36 35219 cdlemk38 35221 cdlemkid 35242 cdlemk19x 35249 cdlemk11t 35252 |
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