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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfunidALT | Structured version Visualization version GIF version |
Description: Deduction version of nfuni 4839. (Contributed by NM, 19-Nov-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfunidALT.1 | ⊢ (𝜑 → Ⅎ𝑥𝐴) |
Ref | Expression |
---|---|
nfunidALT | ⊢ (𝜑 → Ⅎ𝑥∪ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfunidALT.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝐴) | |
2 | abidnf 3694 | . . 3 ⊢ (Ⅎ𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦 ∈ 𝐴} = 𝐴) | |
3 | 2 | unieqd 4842 | . 2 ⊢ (Ⅎ𝑥𝐴 → ∪ {𝑦 ∣ ∀𝑥 𝑦 ∈ 𝐴} = ∪ 𝐴) |
4 | nfaba1 2986 | . . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥 𝑦 ∈ 𝐴} | |
5 | 4 | nfuni 4839 | . 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥 𝑦 ∈ 𝐴} |
6 | 1, 3, 5 | nfded 36097 | 1 ⊢ (𝜑 → Ⅎ𝑥∪ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 ∈ wcel 2110 {cab 2799 Ⅎwnfc 2961 ∪ cuni 4832 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-uni 4833 |
This theorem is referenced by: (None) |
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