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| Mirrors > Home > MPE Home > Th. List > nfwrd | Structured version Visualization version GIF version | ||
| Description: Hypothesis builder for Word 𝑆. (Contributed by Mario Carneiro, 26-Feb-2016.) |
| Ref | Expression |
|---|---|
| nfwrd.1 | ⊢ Ⅎ𝑥𝑆 |
| Ref | Expression |
|---|---|
| nfwrd | ⊢ Ⅎ𝑥Word 𝑆 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-word 14553 | . 2 ⊢ Word 𝑆 = {𝑤 ∣ ∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆} | |
| 2 | nfcv 2905 | . . . 4 ⊢ Ⅎ𝑥ℕ0 | |
| 3 | nfcv 2905 | . . . . 5 ⊢ Ⅎ𝑥𝑤 | |
| 4 | nfcv 2905 | . . . . 5 ⊢ Ⅎ𝑥(0..^𝑙) | |
| 5 | nfwrd.1 | . . . . 5 ⊢ Ⅎ𝑥𝑆 | |
| 6 | 3, 4, 5 | nff 6732 | . . . 4 ⊢ Ⅎ𝑥 𝑤:(0..^𝑙)⟶𝑆 |
| 7 | 2, 6 | nfrexw 3313 | . . 3 ⊢ Ⅎ𝑥∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆 |
| 8 | 7 | nfab 2911 | . 2 ⊢ Ⅎ𝑥{𝑤 ∣ ∃𝑙 ∈ ℕ0 𝑤:(0..^𝑙)⟶𝑆} |
| 9 | 1, 8 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥Word 𝑆 |
| Colors of variables: wff setvar class |
| Syntax hints: {cab 2714 Ⅎwnfc 2890 ∃wrex 3070 ⟶wf 6557 (class class class)co 7431 0cc0 11155 ℕ0cn0 12526 ..^cfzo 13694 Word cword 14552 |
| 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-3an 1089 df-tru 1543 df-fal 1553 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-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-br 5144 df-opab 5206 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-fun 6563 df-fn 6564 df-f 6565 df-word 14553 |
| This theorem is referenced by: (None) |
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