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 1043 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜓)) | |
2 | 1 | anbi2i 730 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓))) |
3 | bnj252 30769 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃))) | |
4 | bnj252 30769 | . 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ (𝜒 ∧ 𝜃 ∧ 𝜓))) | |
5 | 2, 3, 4 | 3bitr4i 292 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓)) |
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: bnj291 30777 bnj334 30779 |
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