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Mirrors > Home > MPE Home > Th. List > a1dd | Structured version Visualization version GIF version |
Description: Double deduction introducing an antecedent. Deduction associated with a1d 25. Double deduction associated with ax-1 6 and a1i 11. (Contributed by NM, 17-Dec-2004.) (Proof shortened by Mel L. 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 34 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
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