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Mirrors > Home > MPE Home > Th. List > biimprd | Structured version Visualization version GIF version |
Description: Deduce a converse implication from a logical equivalence. Deduction associated with biimpr 223 and biimpri 231. (Contributed by NM, 11-Jan-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.) |
Ref | Expression |
---|---|
biimprd.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
biimprd | ⊢ (𝜑 → (𝜒 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝜒 → 𝜒) | |
2 | biimprd.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | syl5ibr 249 | 1 ⊢ (𝜑 → (𝜒 → 𝜓)) |
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