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Mirrors > Home > MPE Home > Th. List > nfcriv | Structured version Visualization version GIF version |
Description: Consequence of the not-free predicate, similiar to nfcri 2968. Requires 𝑦 and 𝐴 be disjoint, but is not based on ax-13 2381. (Contributed by Wolf Lammen, 13-May-2023.) |
Ref | Expression |
---|---|
nfcriv.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfcriv | ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcriv.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcr 2963 | . 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: 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-12 2167 |
This theorem depends on definitions: df-bi 208 df-ex 1772 df-nfc 2960 |
This theorem is referenced by: nfcrii 2967 nfnfc 2987 cleqf 3007 nfccdeq 3766 csbgfi 3900 dfss2f 3955 iunxsngf 5005 fedgmullem2 30925 |
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