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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 2373 from nfsab1 2718. UPDATE / TODO: nfsab1 2718 does not use ax-13 2373 either anymore; bj-nfsab1 36759 is shorter than nfsab1 2718 but uses ax-12 2173. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfsab1 | ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbab1 2719 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | 1 | nf5i 2142 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1778 ∈ wcel 2104 {cab 2710 |
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 1963 ax-7 2003 ax-10 2137 ax-12 2173 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-ex 1775 df-nf 1779 df-sb 2061 df-clab 2711 |
This theorem is referenced by: (None) |
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