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Mirrors > Home > MPE Home > Th. List > pm4.71rd | Structured version Visualization version GIF version |
Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 10-Feb-2005.) |
Ref | Expression |
---|---|
pm4.71rd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
pm4.71rd | ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71rd.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | pm4.71r 551 | . 2 ⊢ ((𝜓 → 𝜒) ↔ (𝜓 ↔ (𝜒 ∧ 𝜓))) | |
3 | 1, 2 | sylib 210 | 1 ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜓))) |
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