Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj707 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj707.1 | ⊢ (𝜒 → 𝜏) |
Ref | Expression |
---|---|
bnj707 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj258 30027 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒)) | |
2 | 1 | simprbi 479 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜒) |
3 | bnj707.1 | . 2 ⊢ (𝜒 → 𝜏) | |
4 | 2, 3 | syl 17 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 ∧ 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: bnj771 30088 bnj998 30280 bnj1001 30282 bnj1006 30283 bnj1053 30298 bnj1121 30307 bnj1030 30309 |
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