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Mirrors > Home > MPE Home > Th. List > nfcvf2 | Structured version Visualization version GIF version |
Description: If 𝑥 and 𝑦 are distinct, then 𝑦 is not free in 𝑥. (Contributed by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
nfcvf2 | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑦𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcvf 2960 | . 2 ⊢ (¬ ∀𝑦 𝑦 = 𝑥 → Ⅎ𝑦𝑥) | |
2 | 1 | naecoms 2395 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑦𝑥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1599 Ⅎwnfc 2919 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-nfc 2921 |
This theorem is referenced by: dfid3 5262 oprabid 6953 axrepndlem1 9749 axrepndlem2 9750 axrepnd 9751 axunnd 9753 axpowndlem3 9756 axpowndlem4 9757 axpownd 9758 axregndlem2 9760 axinfndlem1 9762 axinfnd 9763 axacndlem4 9767 axacndlem5 9768 axacnd 9769 bj-nfcsym 33457 |
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