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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 6509 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑦𝐴𝐹𝑦) | |
2 | dfiota2 6454 | . 2 ⊢ (℩𝑦𝐴𝐹𝑦) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} | |
3 | 1, 2 | eqtri 2765 | 1 ⊢ (𝐹‘𝐴) = ∪ {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦 ↔ 𝑦 = 𝑥)} |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1540 = wceq 1542 {cab 2714 ∪ cuni 4870 class class class wbr 5110 ℩cio 6451 ‘cfv 6501 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-v 3450 df-in 3922 df-ss 3932 df-sn 4592 df-uni 4871 df-iota 6453 df-fv 6509 |
This theorem is referenced by: elfv 6845 |
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