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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 1796 | . . 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 | nfriotadw 7111 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑)) |
7 | 6 | mptru 1535 | 1 ⊢ Ⅎ𝑥(℩𝑦 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1529 Ⅎwnf 1775 Ⅎwnfc 2958 ℩crio 7102 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-sn 4558 df-uni 4831 df-iota 6307 df-riota 7103 |
This theorem is referenced by: csbriota 7118 nfoi 8966 lble 11581 nosupbnd1 33111 riotasvd 35972 riotasv2d 35973 riotasv2s 35974 cdleme26ee 37376 cdleme31sn1 37397 cdlemefs32sn1aw 37430 cdleme43fsv1snlem 37436 cdleme41sn3a 37449 cdleme32d 37460 cdleme32f 37462 cdleme40m 37483 cdleme40n 37484 cdlemk36 37929 cdlemk38 37931 cdlemkid 37952 cdlemk19x 37959 cdlemk11t 37962 |
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