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| Mirrors > Home > MPE Home > Th. List > anbi2i | Structured version Visualization version GIF version | ||
| Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 16-Nov-2013.) |
| Ref | Expression |
|---|---|
| anbi.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| anbi2i | ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anbi.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜒 → (𝜑 ↔ 𝜓)) |
| 3 | 2 | pm5.32i 574 | 1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓)) |
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