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Mirrors > Home > MPE Home > Th. List > nfabdOLD | Structured version Visualization version GIF version |
Description: Obsolete version of nfabd 3001 as of 10-May-2023. (Contributed by Mario Carneiro, 8-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfabdOLD.1 | ⊢ Ⅎ𝑦𝜑 |
nfabdOLD.2 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Ref | Expression |
---|---|
nfabdOLD | ⊢ (𝜑 → Ⅎ𝑥{𝑦 ∣ 𝜓}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfabdOLD.1 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfabdOLD.2 | . . 3 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
3 | 2 | adantr 483 | . 2 ⊢ ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓) |
4 | 1, 3 | nfabd2 3002 | 1 ⊢ (𝜑 → Ⅎ𝑥{𝑦 ∣ 𝜓}) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1535 Ⅎwnf 1784 {cab 2799 Ⅎwnfc 2961 |
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-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-13 2390 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 |
This theorem is referenced by: (None) |
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