Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj836 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj836.1 | ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) |
bnj836.2 | ⊢ (𝜓 → 𝜏) |
Ref | Expression |
---|---|
bnj836 | ⊢ (𝜂 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj836.1 | . 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) | |
2 | bnj836.2 | . . 3 ⊢ (𝜓 → 𝜏) | |
3 | 2 | 3ad2ant2 1136 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
4 | 1, 3 | sylbi 220 | 1 ⊢ (𝜂 → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∧ w3a 1089 |
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 210 df-an 400 df-3an 1091 |
This theorem is referenced by: bnj1379 32523 bnj1175 32697 bnj1286 32712 bnj1450 32743 bnj1501 32760 bnj1523 32764 |
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