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Mirrors > Home > ILE 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 5 | . 2 ⊢ (𝜒 → (𝜃 → 𝜒)) | |
3 | 1, 2 | syl6 29 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: nnsub 7952 difelfzle 8992 bj-inf2vnlem2 10096 |
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