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Metamath Proof Explorer
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996)
|
|
Ref |
Expression |
|
Hypothesis |
anabss4.1 |
⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 ) |
|
Assertion |
anabss4 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
anabss4.1 |
⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 ) |
| 2 |
1
|
anabss1 |
⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) |
| 3 |
2
|
ancoms |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |