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| Mirrors > Home > MPE Home > Th. List > biantrurd | Structured version Visualization version GIF version | ||
| Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 1-May-1995.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
| Ref | Expression |
|---|---|
| biantrud.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| biantrurd | ⊢ (𝜑 → (𝜒 ↔ (𝜓 ∧ 𝜒))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biantrud.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | ibar 528 | . 2 ⊢ (𝜓 → (𝜒 ↔ (𝜓 ∧ 𝜒))) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜒 ↔ (𝜓 ∧ 𝜒))) |
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