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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj290 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj290 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anrot 1085 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜓)) | |
2 | 1 | anbi2i 616 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓))) |
3 | bnj252 31371 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃))) | |
4 | bnj252 31371 | . 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓))) | |
5 | 2, 3, 4 | 3bitr4i 295 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 ∧ wa 386 ∧ w3a 1071 ∧ w-bnj17 31354 |
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 199 df-an 387 df-3an 1073 df-bnj17 31355 |
This theorem is referenced by: bnj291 31379 bnj334 31381 |
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