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Mirrors > Home > ILE Home > Th. List > 2eu2ex | GIF version |
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2eu2ex | ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 1930 | . 2 ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃!𝑦𝜑) | |
2 | euex 1930 | . . 3 ⊢ (∃!𝑦𝜑 → ∃𝑦𝜑) | |
3 | 2 | eximi 1491 | . 2 ⊢ (∃𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
4 | 1, 3 | syl 14 | 1 ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1381 ∃!weu 1900 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 |
This theorem is referenced by: (None) |
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