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Mirrors > Home > MPE Home > Th. List > nfiota1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfiota1 | ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiota2 6284 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
2 | nfaba1 2963 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
3 | 2 | nfuni 4807 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
4 | 1, 3 | nfcxfr 2953 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∀wal 1536 {cab 2776 Ⅎwnfc 2936 ∪ cuni 4800 ℩cio 6281 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ral 3111 df-rex 3112 df-v 3443 df-in 3888 df-ss 3898 df-sn 4526 df-uni 4801 df-iota 6283 |
This theorem is referenced by: iota2df 6311 sniota 6315 opabiota 6721 nfriota1 7100 nfriotadw 7101 nfriotad 7104 erovlem 8376 bnj1366 32211 nosupbnd2 33329 |
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