Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | dfvd2an | ⊢ ( ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vd1 | ⊢ ( ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ( ( 𝜑 , 𝜓 ) → 𝜒 ) ) | |
2 | df-vhc2 | ⊢ ( ( 𝜑 , 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ) ) | |
3 | 2 | imbi1i | ⊢ ( ( ( 𝜑 , 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) |
4 | 1 3 | bitri | ⊢ ( ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) |