a1d - Intuitionistic Logic Explorer
Hypothesis
Ref | Expression |
---|---|
a1d.1 | ⊢(𝜑→𝜓) |
Assertion
Ref | Expression |
---|---|
a1d | ⊢(𝜑→(𝜒→𝜓)) |
Proof of Theorem a1d
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 | ⊢(𝜓→(𝜒→𝜓)) | |
2 | ax-1 | ⊢( (𝜓→(𝜒→𝜓)) → (𝜑→(𝜓→(𝜒→𝜓))) ) | |
3 | 1, 2 | ax-mp | ⊢(𝜑→(𝜓→(𝜒→𝜓))) |
4 | ax-2 | ⊢( (𝜑→(𝜓→(𝜒→𝜓))) → ((𝜑→𝜓)→(𝜑→(𝜒→𝜓))) ) | |
5 | 3, 4 | ax-mp | ⊢( (𝜑→𝜓) → (𝜑→(𝜒→𝜓)) ) |
6 | a1d.1 | ⊢(𝜑→𝜓) | |
7 | 5, 6 | ax-mp | ⊢(𝜑→(𝜒→𝜓)) |