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Mirrors > Home > ILE Home > Th. List > df-1st | GIF version |
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 6161 proves that it does this. For example, (1st ‘〈 3 , 4 〉) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 5122 and op1stb 4490). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.) |
Ref | Expression |
---|---|
df-1st | ⊢ 1st = (𝑥 ∈ V ↦ ∪ dom {𝑥}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | c1st 6153 | . 2 class 1st | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 2749 | . . 3 class V | |
4 | 2 | cv 1362 | . . . . . 6 class 𝑥 |
5 | 4 | csn 3604 | . . . . 5 class {𝑥} |
6 | 5 | cdm 4638 | . . . 4 class dom {𝑥} |
7 | 6 | cuni 3821 | . . 3 class ∪ dom {𝑥} |
8 | 2, 3, 7 | cmpt 4076 | . 2 class (𝑥 ∈ V ↦ ∪ dom {𝑥}) |
9 | 1, 8 | wceq 1363 | 1 wff 1st = (𝑥 ∈ V ↦ ∪ dom {𝑥}) |
Colors of variables: wff set class |
This definition is referenced by: 1stvalg 6157 fo1st 6172 f1stres 6174 |
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