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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj252 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj252 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj250 31068 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) | |
2 | df-3an 1074 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜃)) | |
3 | 2 | anbi2i 732 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) |
4 | 1, 3 | bitr4i 267 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ∧ wa 383 ∧ w3a 1072 ∧ w-bnj17 31053 |
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 385 df-3an 1074 df-bnj17 31054 |
This theorem is referenced by: bnj290 31077 bnj563 31112 bnj919 31136 bnj976 31147 bnj543 31262 bnj570 31274 bnj594 31281 bnj916 31302 bnj917 31303 bnj964 31312 bnj983 31320 bnj984 31321 bnj998 31325 bnj999 31326 bnj1021 31333 bnj1083 31345 bnj1450 31417 |
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