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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 532 | . 2 ⊢ (𝜓 → (𝜒 ↔ (𝜓 ∧ 𝜒))) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜒 ↔ (𝜓 ∧ 𝜒))) |
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