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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 6501 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥) | |
2 | iotauni 6468 | . 2 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) | |
3 | 1, 2 | eqtrid 2789 | 1 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1541 ∃!weu 2567 {cab 2714 ∪ cuni 4863 class class class wbr 5103 ℩cio 6443 ‘cfv 6493 |
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-12 2171 ax-ext 2708 |
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-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-v 3445 df-un 3913 df-in 3915 df-ss 3925 df-sn 4585 df-pr 4587 df-uni 4864 df-iota 6445 df-fv 6501 |
This theorem is referenced by: afveu 45286 |
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