Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | imp5.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) | |
Assertion | imp5g | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( ( 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜂 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp5.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) | |
2 | 1 | imp4b | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → ( 𝜏 → 𝜂 ) ) ) |
3 | 2 | impd | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( ( 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜂 ) ) |