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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vexwv | Structured version Visualization version GIF version |
Description: Version of bj-vexw 32855 with a dv condition, which does not require ax-13 2246. The degenerate instance of bj-vexw 32855 is a simple consequence of abid 2610 (which does not depend on ax-13 2246 either). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vexwv.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
bj-vexwv | ⊢ 𝑦 ∈ {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vexwvt 32856 | . 2 ⊢ (∀𝑥𝜑 → 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | bj-vexwv.1 | . 2 ⊢ 𝜑 | |
3 | 1, 2 | mpg 1724 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 {cab 2608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-sb 1881 df-clab 2609 |
This theorem is referenced by: bj-denotes 32858 bj-rexvwv 32866 bj-rababwv 32867 bj-df-v 33016 |
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