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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 5769 | . 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
2 | nfaba1 2756 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} | |
3 | 2 | nfuni 4378 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)} |
4 | 1, 3 | nfcxfr 2749 | 1 ⊢ Ⅎ𝑥(℩𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∀wal 1473 {cab 2596 Ⅎwnfc 2738 ∪ cuni 4372 ℩cio 5766 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-sn 4126 df-uni 4373 df-iota 5768 |
This theorem is referenced by: iota2df 5792 sniota 5795 opabiota 6171 nfriota1 6518 nfriotad 6519 erovlem 7730 bnj1366 30154 |
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