Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | exp512.1 | ⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜏 ) ) ) → 𝜂 ) | |
Assertion | exp512 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp512.1 | ⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜏 ) ) ) → 𝜂 ) | |
2 | 1 | ex | ⊢ ( 𝜑 → ( ( ( 𝜓 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜏 ) ) → 𝜂 ) ) |
3 | 2 | exp5l | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) |