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Mirrors > Home > ILE Home > Th. List > eubidv | GIF version |
Description: Formula-building rule for unique existential quantifier (deduction form). (Contributed by NM, 9-Jul-1994.) |
Ref | Expression |
---|---|
eubidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
eubidv | ⊢ (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1539 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | eubidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | eubid 2045 | 1 ⊢ (𝜑 → (∃!𝑥𝜓 ↔ ∃!𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 105 ∃!weu 2038 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-eu 2041 |
This theorem is referenced by: eubii 2047 eueq2dc 2925 eueq3dc 2926 reuhypd 4489 feu 5417 funfveu 5547 dff4im 5683 acexmid 5895 upxp 14232 dedekindicc 14571 |
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