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Mirrors > Home > NFE Home > Th. List > a1dd | GIF version |
Description: Deduction introducing a nested embedded antecedent. (Contributed by NM, 17-Dec-2004.) (Proof shortened by O'Cat, 15-Jan-2008.) |
Ref | Expression |
---|---|
a1dd.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
a1dd | ⊢ (φ → (ψ → (θ → χ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a1dd.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | ax-1 6 | . 2 ⊢ (χ → (θ → χ)) | |
3 | 1, 2 | syl6 29 | 1 ⊢ (φ → (ψ → (θ → χ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: merco2 1501 ax12b 1689 nfsb4t 2080 lenltfin 4469 tfinltfinlem1 4500 xpexr 5109 eqfnfv 5392 dff3 5420 spacind 6287 |
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