Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > syl6bi | Structured version Visualization version GIF version |
Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994.) |
Ref | Expression |
---|---|
syl6bi.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
syl6bi.2 | ⊢ (𝜒 → 𝜃) |
Ref | Expression |
---|---|
syl6bi | ⊢ (𝜑 → (𝜓 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6bi.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | biimpd 232 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | syl6bi.2 | . 2 ⊢ (𝜒 → 𝜃) | |
4 | 2, 3 | syl6 35 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
Copyright terms: Public domain | W3C validator |