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Mirrors > Home > ILE Home > Th. List > mobidv | GIF version |
Description: Formula-building rule for "at most one" quantifier (deduction form). (Contributed by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
mobidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
mobidv | ⊢ (𝜑 → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1467 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | mobidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | mobid 1984 | 1 ⊢ (𝜑 → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∃*wmo 1950 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-4 1446 ax-17 1465 ax-ial 1473 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-eu 1952 df-mo 1953 |
This theorem is referenced by: mobii 1986 mosubopt 4518 dffun6f 5043 funmo 5045 1stconst 6002 2ndconst 6003 |
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