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Mirrors > Home > MPE Home > Th. List > fveu | Structured version Visualization version GIF version |
Description: The value of a function at a unique point. (Contributed by Scott Fenton, 6-Oct-2017.) |
Ref | Expression |
---|---|
fveu | ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fv 6193 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥) | |
2 | iotauni 6161 | . 2 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) | |
3 | 1, 2 | syl5eq 2819 | 1 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1508 ∃!weu 2584 {cab 2751 ∪ cuni 4708 class class class wbr 4925 ℩cio 6147 ‘cfv 6185 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 ax-5 1870 ax-6 1929 ax-7 1966 ax-8 2053 ax-9 2060 ax-10 2080 ax-11 2094 ax-12 2107 ax-ext 2743 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 835 df-tru 1511 df-ex 1744 df-nf 1748 df-sb 2017 df-mo 2548 df-eu 2585 df-clab 2752 df-cleq 2764 df-clel 2839 df-nfc 2911 df-rex 3087 df-v 3410 df-sbc 3675 df-un 3827 df-sn 4436 df-pr 4438 df-uni 4709 df-iota 6149 df-fv 6193 |
This theorem is referenced by: afveu 42792 |
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