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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj835 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj835.1 | ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) |
bnj835.2 | ⊢ (𝜑 → 𝜏) |
Ref | Expression |
---|---|
bnj835 | ⊢ (𝜂 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj835.1 | . 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) | |
2 | bnj835.2 | . . 3 ⊢ (𝜑 → 𝜏) | |
3 | 2 | 3ad2ant1 1134 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
4 | 1, 3 | sylbi 216 | 1 ⊢ (𝜂 → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ w3a 1088 |
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 206 df-an 398 df-3an 1090 |
This theorem is referenced by: bnj1219 33842 bnj1379 33872 bnj1175 34046 bnj1286 34061 bnj1280 34062 bnj1296 34063 bnj1398 34076 bnj1415 34080 bnj1417 34083 bnj1421 34084 bnj1442 34091 bnj1450 34092 bnj1452 34094 bnj1489 34098 bnj1312 34100 bnj1501 34109 bnj1523 34113 |
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