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Metamath Proof Explorer
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004)
|
|
Ref |
Expression |
|
Hypothesis |
anabsan2.1 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜓 ) ) → 𝜒 ) |
|
Assertion |
anabsan2 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
anabsan2.1 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜓 ) ) → 𝜒 ) |
| 2 |
1
|
an12s |
⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 ) |
| 3 |
2
|
anabss7 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |