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Mirrors > Home > ILE Home > Th. List > exlimdvv | GIF version |
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.) |
Ref | Expression |
---|---|
exlimdvv.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
exlimdvv | ⊢ (φ → (∃x∃yψ → χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimdvv.1 | . . 3 ⊢ (φ → (ψ → χ)) | |
2 | 1 | exlimdv 1697 | . 2 ⊢ (φ → (∃yψ → χ)) |
3 | 2 | exlimdv 1697 | 1 ⊢ (φ → (∃x∃yψ → χ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-5 1333 ax-gen 1335 ax-ie2 1380 ax-17 1416 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: euotd 3982 funopg 4877 th3qlem1 6144 fundmen 6222 addnq0mo 6430 mulnq0mo 6431 genprndl 6504 genprndu 6505 genpdisj 6506 mullocpr 6552 addsrmo 6671 mulsrmo 6672 |
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