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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-abbii | Structured version Visualization version GIF version |
Description: Remove dependency on ax-13 2234 from abbii 2726. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-abbii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
bj-abbii | ⊢ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-abbi 31963 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) ↔ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓}) | |
2 | bj-abbii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpgbi 1716 | 1 ⊢ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓} |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 = wceq 1475 {cab 2596 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 |
This theorem is referenced by: bj-rababwv 32061 |
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