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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 6416 with a disjoint variable condition, which does not require ax-13 2370. (Contributed by NM, 23-Aug-2011.) (Revised by Gino Giotto, 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 6413 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑)) |
5 | 4 | mptru 1546 | 1 ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1540 Ⅎwnf 1783 Ⅎwnfc 2884 ℩cio 6408 |
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 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 846 df-tru 1542 df-ex 1780 df-nf 1784 df-sb 2066 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2886 df-ral 3062 df-rex 3071 df-v 3439 df-in 3899 df-ss 3909 df-sn 4566 df-uni 4845 df-iota 6410 |
This theorem is referenced by: csbiota 6451 nffv 6814 nfsum1 15450 nfsum 15451 nfcprod1 15669 nfcprod 15670 nfafv2 44954 |
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