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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj253 | Structured version Visualization version GIF version | ||
| Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| bnj253 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bnj248 34714 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)) | |
| 2 | df-3an 1089 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)) | |
| 3 | 1, 2 | bitr4i 278 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ↔ wb 206 ∧ wa 395 ∧ w3a 1087 ∧ w-bnj17 34700 | 
| 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 207 df-an 396 df-3an 1089 df-bnj17 34701 | 
| This theorem is referenced by: bnj543 34907 bnj558 34916 bnj594 34926 bnj917 34948 bnj929 34950 bnj944 34952 bnj978 34963 bnj998 34971 bnj1006 34974 | 
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