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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 1130 | . 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 1084 |
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 395 df-3an 1086 |
This theorem is referenced by: bnj1219 34645 bnj1379 34675 bnj1175 34849 bnj1286 34864 bnj1280 34865 bnj1296 34866 bnj1398 34879 bnj1415 34883 bnj1417 34886 bnj1421 34887 bnj1442 34894 bnj1450 34895 bnj1452 34897 bnj1489 34901 bnj1312 34903 bnj1501 34912 bnj1523 34916 |
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