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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 6541 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑦𝐴𝐹𝑦) | |
2 | dfiota2 6486 | . 2 ⊢ (℩𝑦𝐴𝐹𝑦) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} | |
3 | 1, 2 | eqtri 2752 | 1 ⊢ (𝐹‘𝐴) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1531 = wceq 1533 {cab 2701 ∪ cuni 4899 class class class wbr 5138 ℩cio 6483 ‘cfv 6533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-v 3468 df-in 3947 df-ss 3957 df-sn 4621 df-uni 4900 df-iota 6485 df-fv 6541 |
This theorem is referenced by: elfv 6879 |
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