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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 1730 | . . 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 6619 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑)) |
7 | 6 | trud 1493 | 1 ⊢ Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1484 Ⅎwnf 1708 Ⅎwnfc 2751 ℩crio 6610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-sn 4178 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: csbriota 6623 nfoi 8419 lble 10975 nosupbnd1 31860 riotasvd 34242 riotasv2d 34243 riotasv2s 34244 cdleme26ee 35648 cdleme31sn1 35669 cdlemefs32sn1aw 35702 cdleme43fsv1snlem 35708 cdleme41sn3a 35721 cdleme32d 35732 cdleme32f 35734 cdleme40m 35755 cdleme40n 35756 cdlemk36 36201 cdlemk38 36203 cdlemkid 36224 cdlemk19x 36231 cdlemk11t 36234 |
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