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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj291 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj291 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj290 33134 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓)) | |
2 | df-bnj17 33111 | . 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓)) | |
3 | 1, 2 | bitri 274 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 396 ∧ w3a 1087 ∧ w-bnj17 33110 |
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 206 df-an 397 df-3an 1089 df-bnj17 33111 |
This theorem is referenced by: bnj643 33173 bnj938 33361 bnj944 33362 |
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