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Mirrors > Home > MPE Home > Th. List > hbab1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 26-May-1993.) (Proof shortened by Wolf Lammen, 25-Oct-2024.) |
Ref | Expression |
---|---|
hbab1 | ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfsab1 2713 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nf5ri 2184 | 1 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1532 ∈ wcel 2099 {cab 2705 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-10 2130 ax-12 2167 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-ex 1775 df-nf 1779 df-sb 2061 df-clab 2706 |
This theorem is referenced by: eqabbOLD 2870 bnj1317 34446 bnj1318 34650 bj-nfsab1 36287 |
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