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Mirrors > Home > MPE Home > Th. List > fv2 | Structured version Visualization version GIF version |
Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fv2 | ⊢ (𝐹‘𝐴) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fv 6551 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑦𝐴𝐹𝑦) | |
2 | dfiota2 6496 | . 2 ⊢ (℩𝑦𝐴𝐹𝑦) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} | |
3 | 1, 2 | eqtri 2760 | 1 ⊢ (𝐹‘𝐴) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1539 = wceq 1541 {cab 2709 ∪ cuni 4908 class class class wbr 5148 ℩cio 6493 ‘cfv 6543 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-nf 1786 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-v 3476 df-in 3955 df-ss 3965 df-sn 4629 df-uni 4909 df-iota 6495 df-fv 6551 |
This theorem is referenced by: elfv 6889 |
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