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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj645 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj645 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bnj17 32236 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) | |
2 | 1 | simprbi 500 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1088 ∧ w-bnj17 32235 |
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-bnj17 32236 |
This theorem is referenced by: bnj708 32306 bnj908 32482 bnj929 32487 bnj964 32494 bnj1110 32533 |
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