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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 6517 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
2 | nfaba1 2911 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
3 | 2 | nfuni 4919 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
4 | 1, 3 | nfcxfr 2901 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 ∀wal 1535 {cab 2712 Ⅎwnfc 2888 ∪ cuni 4912 ℩cio 6514 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-nf 1781 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ral 3060 df-rex 3069 df-v 3480 df-ss 3980 df-sn 4632 df-uni 4913 df-iota 6516 |
This theorem is referenced by: iota2df 6550 sniota 6554 opabiota 6991 nfriota1 7395 nfriotadw 7396 nfriotad 7399 erovlem 8852 nosupbnd2 27776 noinfbnd2 27791 bnj1366 34822 |
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