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Mirrors > Home > MPE Home > Th. List > nfnfc | Structured version Visualization version GIF version |
Description: Hypothesis builder for Ⅎ𝑦𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.) Remove dependency on ax-13 2390. (Revised by Wolf Lammen, 10-Dec-2019.) |
Ref | Expression |
---|---|
nfnfc.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfnfc | ⊢ Ⅎ𝑥Ⅎ𝑦𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfc 2965 | . 2 ⊢ (Ⅎ𝑦𝐴 ↔ ∀𝑧Ⅎ𝑦 𝑧 ∈ 𝐴) | |
2 | nfnfc.1 | . . . . 5 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfcriv 2969 | . . . 4 ⊢ Ⅎ𝑥 𝑧 ∈ 𝐴 |
4 | 3 | nfnf 2345 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑦 𝑧 ∈ 𝐴 |
5 | 4 | nfal 2342 | . 2 ⊢ Ⅎ𝑥∀𝑧Ⅎ𝑦 𝑧 ∈ 𝐴 |
6 | 1, 5 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥Ⅎ𝑦𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1535 Ⅎwnf 1784 ∈ wcel 2114 Ⅎwnfc 2963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-11 2161 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1781 df-nf 1785 df-nfc 2965 |
This theorem is referenced by: (None) |
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