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| Mirrors > Home > MPE Home > Th. List > nfiotaw | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for the ℩ class. Version of nfiota 6520 with a disjoint variable condition, which does not require ax-13 2377. (Contributed by NM, 23-Aug-2011.) Avoid ax-13 2377. (Revised by GG, 26-Jan-2024.) | 
| Ref | Expression | 
|---|---|
| nfiotaw.1 | ⊢ Ⅎ𝑥𝜑 | 
| Ref | Expression | 
|---|---|
| nfiotaw | ⊢ Ⅎ𝑥(℩𝑦𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nftru 1804 | . . 3 ⊢ Ⅎ𝑦⊤ | |
| 2 | nfiotaw.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
| 3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) | 
| 4 | 1, 3 | nfiotadw 6517 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑)) | 
| 5 | 4 | mptru 1547 | 1 ⊢ Ⅎ𝑥(℩𝑦𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊤wtru 1541 Ⅎwnf 1783 Ⅎwnfc 2890 ℩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: csbiota 6554 nffv 6916 nfsum1 15726 nfsum 15727 nfcprod1 15944 nfcprod 15945 nfafv2 47230 | 
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