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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 6045 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥) | |
2 | iotauni 6012 | . 2 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) | |
3 | 1, 2 | syl5eq 2794 | 1 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1620 ∃!weu 2595 {cab 2734 ∪ cuni 4576 class class class wbr 4792 ℩cio 5998 ‘cfv 6037 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1859 ax-4 1874 ax-5 1976 ax-6 2042 ax-7 2078 ax-9 2136 ax-10 2156 ax-11 2171 ax-12 2184 ax-13 2379 ax-ext 2728 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1623 df-ex 1842 df-nf 1847 df-sb 2035 df-eu 2599 df-clab 2735 df-cleq 2741 df-clel 2744 df-nfc 2879 df-rex 3044 df-v 3330 df-sbc 3565 df-un 3708 df-sn 4310 df-pr 4312 df-uni 4577 df-iota 6000 df-fv 6045 |
This theorem is referenced by: afveu 41708 |
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