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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 2753 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 2031 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 2153 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1779 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1481 Ⅎwnf 1708 ∈ wcel 1990 Ⅎwnfc 2751 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-nfc 2753 |
This theorem is referenced by: vtoclgft 3254 vtoclgftOLD 3255 sbcralt 3510 sbcrext 3511 sbcrextOLD 3512 csbiebt 3553 nfopd 4419 nfimad 5475 nffvd 6200 nfded 34254 nfded2 34255 nfunidALT2 34256 |
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