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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 2938 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 2155 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 2331 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1854 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1536 Ⅎwnf 1785 ∈ wcel 2111 Ⅎwnfc 2936 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2142 ax-11 2158 ax-12 2175 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-ex 1782 df-nf 1786 df-nfc 2938 |
This theorem is referenced by: vtoclgft 3501 vtoclgftOLD 3502 sbcralt 3801 sbcrext 3802 csbiebt 3857 nfopd 4782 nfimad 5905 nffvd 6657 wl-dfrmof 35020 wl-dfrabf 35029 nfded 36263 nfded2 36264 nfunidALT2 36265 |
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