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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj251 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj251 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj250 30020 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃))) | |
2 | anass 679 | . . 3 ⊢ (((𝜓 ∧ 𝜒) ∧ 𝜃) ↔ (𝜓 ∧ (𝜒 ∧ 𝜃))) | |
3 | 2 | anbi2i 726 | . 2 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃)))) |
4 | 1, 3 | bitri 263 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∧ wa 383 ∧ w-bnj17 30005 |
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 196 df-an 385 df-3an 1033 df-bnj17 30006 |
This theorem is referenced by: bnj255 30024 bnj535 30214 bnj570 30229 bnj953 30263 bnj1110 30304 |
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