Description: Constructor rule for -/\ . (Contributed by Anthony Hart, 2-Sep-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | nabi1i.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
nabi1i.2 | ⊢ ( 𝜓 ⊼ 𝜒 ) | ||
Assertion | nabi1i | ⊢ ( 𝜑 ⊼ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nabi1i.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
2 | nabi1i.2 | ⊢ ( 𝜓 ⊼ 𝜒 ) | |
3 | 1 | bicomi | ⊢ ( 𝜓 ↔ 𝜑 ) |
4 | 3 | nanbi1i | ⊢ ( ( 𝜓 ⊼ 𝜒 ) ↔ ( 𝜑 ⊼ 𝜒 ) ) |
5 | 2 4 | mpbi | ⊢ ( 𝜑 ⊼ 𝜒 ) |