Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > syl2anc | Structured version Visualization version GIF version |
Description: Syllogism inference combined with contraction. (Contributed by NM, 16-Mar-2012.) |
Ref | Expression |
---|---|
syl2anc.1 | ⊢ (𝜑 → 𝜓) |
syl2anc.2 | ⊢ (𝜑 → 𝜒) |
syl2anc.3 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
syl2anc | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl2anc.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | syl2anc.2 | . 2 ⊢ (𝜑 → 𝜒) | |
3 | syl2anc.3 | . . 3 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
4 | 3 | ex 413 | . 2 ⊢ (𝜓 → (𝜒 → 𝜃)) |
5 | 1, 2, 4 | sylc 65 | 1 ⊢ (𝜑 → 𝜃) |
Copyright terms: Public domain | W3C validator |