Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 . Double deduction associated with com13 . (Contributed by Jeff Hankins, 28-Jun-2009)
Ref | Expression | ||
---|---|---|---|
Hypothesis | com5.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) | |
Assertion | com35 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → ( 𝜃 → ( 𝜒 → 𝜂 ) ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) ) | |
2 | 1 | com34 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) ) ) ) |
3 | 2 | com45 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → ( 𝜏 → ( 𝜒 → 𝜂 ) ) ) ) ) |
4 | 3 | com34 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → ( 𝜃 → ( 𝜒 → 𝜂 ) ) ) ) ) |