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Mathbox for Jonathan Ben-Naim |
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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 32080 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)) | |
2 | df-3an 1086 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)) | |
3 | 1, 2 | 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: bnj543 32275 bnj558 32284 bnj594 32294 bnj917 32316 bnj929 32318 bnj944 32320 bnj978 32331 bnj998 32339 bnj1006 32342 |
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