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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 2376 from nfsab1 2721. UPDATE / TODO: nfsab1 2721 does not use ax-13 2376 either anymore; bj-nfsab1 36795 is shorter than nfsab1 2721 but uses ax-12 2177. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| bj-nfsab1 | ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbab1 2722 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
| 2 | 1 | nf5i 2146 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
| Colors of variables: wff setvar class |
| Syntax hints: Ⅎwnf 1783 ∈ wcel 2108 {cab 2713 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 df-sb 2065 df-clab 2714 |
| This theorem is referenced by: (None) |
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