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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 2891 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 2180 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 2300 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1928 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1630 Ⅎwnf 1857 ∈ wcel 2139 Ⅎwnfc 2889 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-10 2168 ax-11 2183 ax-12 2196 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-ex 1854 df-nf 1859 df-nfc 2891 |
This theorem is referenced by: vtoclgft 3394 vtoclgftOLD 3395 sbcralt 3651 sbcrext 3652 sbcrextOLD 3653 csbiebt 3694 nfopd 4570 nfimad 5633 nffvd 6361 nfded 34757 nfded2 34758 nfunidALT2 34759 |
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