Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | exp5o.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) | |
Assertion | exp5o | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp5o.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( ( 𝜃 ∧ 𝜏 ) → 𝜂 ) ) | |
2 | 1 | expd | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) |
3 | 2 | 3exp | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |