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| Mirrors > Home > MPE Home > Th. List > nfnfc1 | Structured version Visualization version GIF version | ||
| Description: The setvar 𝑥 is bound in Ⅎ𝑥𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.) |
| Ref | Expression |
|---|---|
| nfnfc1 | ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-nfc 2892 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
| 2 | nfnf1 2154 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
| 3 | 2 | nfal 2323 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
| 4 | 1, 3 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
| Colors of variables: wff setvar class |
| Syntax hints: ∀wal 1538 Ⅎwnf 1783 ∈ wcel 2108 Ⅎwnfc 2890 |
| 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-10 2141 ax-11 2157 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 df-nfc 2892 |
| This theorem is referenced by: cbvexeqsetf 3495 sbcralt 3872 sbcrext 3873 csbiebt 3928 nfopd 4890 nfimad 6087 nffvd 6918 wl-issetft 37583 nfded 38968 nfded2 38969 nfunidALT2 38970 |
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