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Mirrors > Home > MPE Home > Th. List > Mathboxes > eliminable-velab | Structured version Visualization version GIF version |
Description: A theorem used to prove the base case of the Eliminability Theorem (see section comment): variable belongs to abstraction. (Contributed by BJ, 30-Apr-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eliminable-velab | ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clab 2713 | 1 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 [wsb 2070 ∈ wcel 2110 {cab 2712 |
This theorem depends on definitions: df-clab 2713 |
This theorem is referenced by: eliminable-veqab 34744 eliminable-abeqv 34745 eliminable-abeqab 34746 eliminable-abelab 34748 |
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