Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vexwv | Structured version Visualization version GIF version |
Description: Version of bj-vexw 32049 with a dv condition, which does not require ax-13 2234. The degenerate instance of bj-vexw 32049 is a simple consequence of abid 2598 (which does not depend on ax-13 2234 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 32050 | . 2 ⊢ (∀𝑥𝜑 → 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | bj-vexwv.1 | . 2 ⊢ 𝜑 | |
3 | 1, 2 | mpg 1715 | 1 ⊢ 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 {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-12 2034 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-sb 1868 df-clab 2597 |
This theorem is referenced by: bj-denotes 32052 bj-rexvwv 32060 bj-rababwv 32061 bj-df-v 32207 |
Copyright terms: Public domain | W3C validator |