syl5 - Metamath Proof Explorer
syl5 - Intuitionistic Logic Explorer
Hypothesis
Ref | Expression |
---|---|
syl5.1 | ⊢(𝜑→𝜓) |
syl5.2 | ⊢(𝜒→(𝜓→𝜃)) |
Assertion
Ref | Expression |
---|---|
syl5 | ⊢(𝜒→(𝜑→𝜃)) |
Proof of Theorem com12
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5.1 | ⊢(𝜑→𝜓) | |
2 | 1 | a1i | ⊢(𝜒→(𝜑→𝜓)) |
3 | syl5.2 | ⊢(𝜒→(𝜓→𝜃)) | |
4 | 3 | a1i | ⊢(𝜒→(𝜑→(𝜓→𝜃))) |
5 | 4 | a2d | ⊢(𝜒→((𝜑→𝜓)→(𝜑→𝜃))) |
6 | 5 | a2i | ⊢( (𝜒→(𝜑→𝜓)) → (𝜒→(𝜑→𝜃)) ) |
7 | 2, 6 | ax-mp | ⊢(𝜒→(𝜑→𝜃)) |