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Mirrors > Home > MPE Home > Th. List > nfopab | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for class abstraction. (Contributed by NM, 1-Sep-1999.) Remove disjoint variable conditions. (Revised by Andrew Salmon, 11-Jul-2011.) (Revised by Scott Fenton, 26-Oct-2024.) |
Ref | Expression |
---|---|
nfopab.1 | ⊢ Ⅎ𝑧𝜑 |
Ref | Expression |
---|---|
nfopab | ⊢ Ⅎ𝑧{〈𝑥, 𝑦〉 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1798 | . . 3 ⊢ Ⅎ𝑥⊤ | |
2 | nftru 1798 | . . 3 ⊢ Ⅎ𝑦⊤ | |
3 | nfopab.1 | . . . 4 ⊢ Ⅎ𝑧𝜑 | |
4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑧𝜑) |
5 | 1, 2, 4 | nfopabd 5206 | . 2 ⊢ (⊤ → Ⅎ𝑧{〈𝑥, 𝑦〉 ∣ 𝜑}) |
6 | 5 | mptru 1540 | 1 ⊢ Ⅎ𝑧{〈𝑥, 𝑦〉 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1534 Ⅎwnf 1777 Ⅎwnfc 2875 {copab 5200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-opab 5201 |
This theorem is referenced by: nfmpt 5245 csbopab 5545 csbopabgALT 5546 nfxp 5699 nfco 5855 nfcnv 5868 nfofr 7670 fineqvrep 34584 |
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