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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj257 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj257 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 460 | . . 3 ⊢ ((𝜒 ∧ 𝜃) ↔ (𝜃 ∧ 𝜒)) | |
2 | 1 | anbi2i 622 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜃 ∧ 𝜒))) |
3 | bnj256 34246 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃))) | |
4 | bnj256 34246 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ (𝜃 ∧ 𝜒))) | |
5 | 2, 3, 4 | 3bitr4i 303 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 395 ∧ w-bnj17 34226 |
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 396 df-3an 1086 df-bnj17 34227 |
This theorem is referenced by: bnj258 34248 bnj334 34253 bnj543 34433 bnj929 34476 |
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