Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 18-Nov-2013)
Ref | Expression | ||
---|---|---|---|
Hypothesis | anabsi7.1 | ⊢ ( 𝜓 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) | |
Assertion | anabsi7 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabsi7.1 | ⊢ ( 𝜓 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) | |
2 | 1 | anabsi6 | ⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) |
3 | 2 | ancoms | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |