| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| 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 6515 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
| 2 | nfaba1 2913 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
| 3 | 2 | nfuni 4914 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
| 4 | 1, 3 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ∀wal 1538 {cab 2714 Ⅎwnfc 2890 ∪ cuni 4907 ℩cio 6512 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ral 3062 df-rex 3071 df-v 3482 df-ss 3968 df-sn 4627 df-uni 4908 df-iota 6514 |
| This theorem is referenced by: iota2df 6548 sniota 6552 opabiota 6991 nfriota1 7395 nfriotadw 7396 nfriotad 7399 erovlem 8853 nosupbnd2 27761 noinfbnd2 27776 bnj1366 34843 |
| Copyright terms: Public domain | W3C validator |