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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 6496 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
2 | nfaba1 2910 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
3 | 2 | nfuni 4915 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
4 | 1, 3 | nfcxfr 2900 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1538 {cab 2708 Ⅎwnfc 2882 ∪ cuni 4908 ℩cio 6493 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-nf 1785 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ral 3061 df-rex 3070 df-v 3475 df-in 3955 df-ss 3965 df-sn 4629 df-uni 4909 df-iota 6495 |
This theorem is referenced by: iota2df 6530 sniota 6534 opabiota 6974 nfriota1 7375 nfriotadw 7376 nfriotad 7380 erovlem 8813 nosupbnd2 27470 noinfbnd2 27485 bnj1366 34153 |
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