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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 2890 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 2152 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 2322 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1850 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1535 Ⅎwnf 1780 ∈ wcel 2106 Ⅎwnfc 2888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-10 2139 ax-11 2155 ax-12 2175 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-ex 1777 df-nf 1781 df-nfc 2890 |
This theorem is referenced by: cbvexeqsetf 3493 sbcralt 3881 sbcrext 3882 csbiebt 3938 nfopd 4895 nfimad 6089 nffvd 6919 wl-issetft 37563 nfded 38949 nfded2 38950 nfunidALT2 38951 |
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