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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfsab1 | Structured version Visualization version GIF version |
Description: Remove dependency on ax-13 2344 from nfsab1 2784. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfsab1 | ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbab1 33692 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | 1 | nf5i 2117 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1765 ∈ wcel 2081 {cab 2775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-10 2112 ax-12 2141 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 |
This theorem is referenced by: bj-abbi 33696 bj-nfab1 33705 |
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