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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 32081 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) | |
2 | df-3an 1086 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜃)) | |
3 | 2 | anbi2i 625 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) |
4 | 1, 3 | bitr4i 281 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∧ wa 399 ∧ w3a 1084 ∧ w-bnj17 32066 |
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 210 df-an 400 df-3an 1086 df-bnj17 32067 |
This theorem is referenced by: bnj290 32090 bnj563 32124 bnj919 32148 bnj976 32159 bnj543 32275 bnj570 32287 bnj594 32294 bnj916 32315 bnj917 32316 bnj964 32325 bnj983 32333 bnj984 32334 bnj998 32339 bnj999 32340 bnj1021 32348 bnj1083 32360 bnj1450 32432 |
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