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Metamath Proof Explorer
Description: Associative law for conjunction applied to antecedent (eliminates
syllogism). (Contributed by NM, 15-Nov-2002)
|
|
Ref |
Expression |
|
Hypothesis |
anasss.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
anasss |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
anasss.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
| 2 |
1
|
exp31 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 3 |
2
|
imp32 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 ) |