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Mirrors > Home > MPE Home > Th. List > pm5.74rd | Structured version Visualization version GIF version |
Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997.) |
Ref | Expression |
---|---|
pm5.74rd.1 | ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) |
Ref | Expression |
---|---|
pm5.74rd | ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.74rd.1 | . 2 ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) | |
2 | pm5.74 273 | . 2 ⊢ ((𝜓 → (𝜒 ↔ 𝜃)) ↔ ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) | |
3 | 1, 2 | sylibr 237 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 |
This theorem is referenced by: pm5.35 826 wl-dral1d 35427 |
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