Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj258 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj258 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj257 31979 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒)) | |
2 | df-bnj17 31959 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒)) | |
3 | 1, 2 | bitri 277 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∧ wa 398 ∧ w3a 1083 ∧ w-bnj17 31958 |
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 209 df-an 399 df-3an 1085 df-bnj17 31959 |
This theorem is referenced by: bnj707 32028 bnj1019 32053 bnj556 32174 bnj594 32186 bnj1018g 32237 bnj1018 32238 bnj1110 32256 |
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