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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 2960 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 2149 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 2333 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1844 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1526 Ⅎwnf 1775 ∈ wcel 2105 Ⅎwnfc 2958 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-11 2151 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-ex 1772 df-nf 1776 df-nfc 2960 |
This theorem is referenced by: vtoclgft 3551 vtoclgftOLD 3552 sbcralt 3852 sbcrext 3853 csbiebt 3909 nfopd 4812 nfimad 5931 nffvd 6675 wl-dfrmof 34736 wl-dfrabf 34745 nfded 35983 nfded2 35984 nfunidALT2 35985 |
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