Description: Constructor rule for -/\ . (Contributed by Anthony Hart, 2-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | naim1i.1 | ⊢ ( 𝜑 → 𝜓 ) | |
naim1i.2 | ⊢ ( 𝜓 ⊼ 𝜒 ) | ||
Assertion | naim1i | ⊢ ( 𝜑 ⊼ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | naim1i.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | naim1i.2 | ⊢ ( 𝜓 ⊼ 𝜒 ) | |
3 | naim1 | ⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 ⊼ 𝜒 ) → ( 𝜑 ⊼ 𝜒 ) ) ) | |
4 | 1 2 3 | mp2 | ⊢ ( 𝜑 ⊼ 𝜒 ) |