Description: Stacked hypotheseis implies goal. (Contributed by Stanislas Polu, 9-Mar-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | syldbl2.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜓 → 𝜃 ) ) | |
Assertion | syldbl2 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syldbl2.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜓 → 𝜃 ) ) | |
2 | 1 | com12 | ⊢ ( 𝜓 → ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) ) |
3 | 2 | anabsi7 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |