| Mathbox for Jonathan Ben-Naim |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj770 | Structured version Visualization version GIF version | ||
| Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj770.1 | ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃)) |
| bnj770.2 | ⊢ (𝜓 → 𝜏) |
| Ref | Expression |
|---|---|
| bnj770 | ⊢ (𝜂 → 𝜏) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj770.1 | . 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃)) | |
| 2 | bnj770.2 | . . 3 ⊢ (𝜓 → 𝜏) | |
| 3 | 2 | bnj706 34768 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
| 4 | 1, 3 | sylbi 217 | 1 ⊢ (𝜂 → 𝜏) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ↔ wb 206 ∧ w-bnj17 34700 |
| 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 207 df-an 396 df-3an 1089 df-bnj17 34701 |
| This theorem is referenced by: bnj1235 34818 bnj605 34921 bnj607 34930 bnj983 34965 bnj1110 34996 bnj1145 35007 bnj1256 35029 bnj1296 35035 bnj1450 35064 |
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