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Mirrors > Home > ILE Home > Th. List > mobii | GIF version |
Description: Formula-building rule for "at most one" quantifier (inference rule). (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 17-Oct-2016.) |
Ref | Expression |
---|---|
mobii.1 | ⊢ (ψ ↔ χ) |
Ref | Expression |
---|---|
mobii | ⊢ (∃*xψ ↔ ∃*xχ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mobii.1 | . . . 4 ⊢ (ψ ↔ χ) | |
2 | 1 | a1i 9 | . . 3 ⊢ ( ⊤ → (ψ ↔ χ)) |
3 | 2 | mobidv 1933 | . 2 ⊢ ( ⊤ → (∃*xψ ↔ ∃*xχ)) |
4 | 3 | trud 1251 | 1 ⊢ (∃*xψ ↔ ∃*xχ) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ⊤ wtru 1243 ∃*wmo 1898 |
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-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-eu 1900 df-mo 1901 |
This theorem is referenced by: moaneu 1973 moanmo 1974 2moswapdc 1987 2exeu 1989 rmobiia 2493 rmov 2568 euxfr2dc 2720 rmoan 2733 2rmorex 2739 mosn 3398 dffun9 4873 funopab 4878 funco 4883 funcnv2 4902 funcnv 4903 fun2cnv 4906 fncnv 4908 imadif 4922 fnres 4958 ovi3 5579 oprabex3 5698 frecuzrdgfn 8879 |
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