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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 6581 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥) | |
2 | iotauni 6548 | . 2 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) | |
3 | 1, 2 | eqtrid 2792 | 1 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∃!weu 2571 {cab 2717 ∪ cuni 4931 class class class wbr 5166 ℩cio 6523 ‘cfv 6573 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-12 2178 ax-ext 2711 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1540 df-ex 1778 df-nf 1782 df-sb 2065 df-mo 2543 df-eu 2572 df-clab 2718 df-cleq 2732 df-clel 2819 df-v 3490 df-un 3981 df-ss 3993 df-sn 4649 df-pr 4651 df-uni 4932 df-iota 6525 df-fv 6581 |
This theorem is referenced by: afveu 47068 |
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