Description: A nested modus ponens inference. Copy of mpi with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | wl-luk-mpi.1 | ⊢ 𝜓 | |
| wl-luk-mpi.2 | ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) | ||
| Assertion | wl-luk-mpi | ⊢ ( 𝜑 → 𝜒 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-luk-mpi.1 | ⊢ 𝜓 | |
| 2 | wl-luk-mpi.2 | ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) | |
| 3 | 1 | wl-luk-a1i | ⊢ ( ¬ 𝜒 → 𝜓 ) |
| 4 | 3 2 | wl-luk-imtrid | ⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜒 ) ) |
| 5 | 4 | wl-luk-pm2.18d | ⊢ ( 𝜑 → 𝜒 ) |