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 6310 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
2 | nfaba1 2986 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
3 | 2 | nfuni 4839 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
4 | 1, 3 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∀wal 1531 {cab 2799 Ⅎwnfc 2961 ∪ cuni 4832 ℩cio 6307 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-sn 4562 df-uni 4833 df-iota 6309 |
This theorem is referenced by: iota2df 6337 sniota 6341 opabiota 6741 nfriota1 7115 nfriotadw 7116 nfriotad 7119 erovlem 8387 bnj1366 32096 nosupbnd2 33211 |
Copyright terms: Public domain | W3C validator |