Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj250 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj250 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bnj17 30753 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) | |
2 | 3anass 1042 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒))) | |
3 | 2 | anbi1i 731 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ↔ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃)) |
4 | anass 681 | . 2 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) | |
5 | 1, 3, 4 | 3bitri 286 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ∧ wa 384 ∧ w3a 1037 ∧ w-bnj17 30752 |
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 197 df-an 386 df-3an 1039 df-bnj17 30753 |
This theorem is referenced by: bnj251 30768 bnj252 30769 bnj345 30780 |
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