Theorem tsyl-P4.15.RC 427

Description: Inference form of tsyl-P4.15 426. †

Hypotheses

Ref	Expression
tsyl-P4.15.RC.1	⊢ (𝜑 → 𝜓)
tsyl-P4.15.RC.2	⊢ (𝜓 → 𝜒)
tsyl-P4.15.RC.3	⊢ (𝜒 → 𝜗)
tsyl-P4.15.RC.4	⊢ (𝜗 → 𝜏)

Assertion

Ref	Expression
tsyl-P4.15.RC	⊢ (𝜑 → 𝜏)

Proof of Theorem tsyl-P4.15.RC

Step	Hyp	Ref	Expression
1		tsyl-P4.15.RC.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
3		tsyl-P4.15.RC.2	. . . 4 ⊢ (𝜓 → 𝜒)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜓 → 𝜒))
5		tsyl-P4.15.RC.3	. . . 4 ⊢ (𝜒 → 𝜗)
6	5	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜒 → 𝜗))
7		tsyl-P4.15.RC.4	. . . 4 ⊢ (𝜗 → 𝜏)
8	7	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜗 → 𝜏))
9	2, 4, 6, 8	tsyl-P4.15 426	. 2 ⊢ (⊤ → (𝜑 → 𝜏))
10	9	ndtruee-P3.18 183	1 ⊢ (𝜑 → 𝜏)

Syntax hints:   → wff-imp 10  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  oroverim-P4.28-L1  465