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Mirrors > Home > MPE Home > Th. List > notbid | Structured version Visualization version GIF version |
Description: Deduction negating both sides of a logical equivalence. (Contributed by NM, 21-May-1994.) |
Ref | Expression |
---|---|
notbid.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
notbid | ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notbid.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | notnotb 318 | . . 3 ⊢ (𝜓 ↔ ¬ ¬ 𝜓) | |
3 | notnotb 318 | . . 3 ⊢ (𝜒 ↔ ¬ ¬ 𝜒) | |
4 | 1, 2, 3 | 3bitr3g 316 | . 2 ⊢ (𝜑 → (¬ ¬ 𝜓 ↔ ¬ ¬ 𝜒)) |
5 | 4 | con4bid 320 | 1 ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒)) |
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