![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 6571 | . 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥) | |
2 | iotauni 6538 | . 2 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) | |
3 | 1, 2 | eqtrid 2787 | 1 ⊢ (∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∪ {𝑥 ∣ 𝐴𝐹𝑥}) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∃!weu 2566 {cab 2712 ∪ cuni 4912 class class class wbr 5148 ℩cio 6514 ‘cfv 6563 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-12 2175 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-nf 1781 df-sb 2063 df-mo 2538 df-eu 2567 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-un 3968 df-ss 3980 df-sn 4632 df-pr 4634 df-uni 4913 df-iota 6516 df-fv 6571 |
This theorem is referenced by: afveu 47103 |
Copyright terms: Public domain | W3C validator |