Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > euimmo | GIF version |
Description: Uniqueness implies "at most one" through implication. (Contributed by NM, 22-Apr-1995.) |
Ref | Expression |
---|---|
euimmo | ⊢ (∀𝑥(𝜑 → 𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2031 | . 2 ⊢ (∃!𝑥𝜓 → ∃*𝑥𝜓) | |
2 | moim 2063 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑)) | |
3 | 1, 2 | syl5 32 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1329 ∃!weu 1999 ∃*wmo 2000 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 |
This theorem is referenced by: euim 2067 2eumo 2087 reuss2 3356 |
Copyright terms: Public domain | W3C validator |