Description: This theorem is in fact a copy of com14 , and repeated here to demonstrate a simple proof scheme. The number '4' in the theorem name indicates that a chain of length 4 is modified.
See wl-impchain-com-1.x for more information how this proof is generated. (Contributed by Wolf Lammen, 7-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | wl-impchain-com-1.4.h1 | ⊢ ( 𝜂 → ( 𝜃 → ( 𝜒 → ( 𝜓 → 𝜑 ) ) ) ) | |
| Assertion | wl-impchain-com-1.4 | ⊢ ( 𝜓 → ( 𝜃 → ( 𝜒 → ( 𝜂 → 𝜑 ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-impchain-com-1.4.h1 | ⊢ ( 𝜂 → ( 𝜃 → ( 𝜒 → ( 𝜓 → 𝜑 ) ) ) ) | |
| 2 | 1 | wl-impchain-com-1.3 | ⊢ ( 𝜒 → ( 𝜃 → ( 𝜂 → ( 𝜓 → 𝜑 ) ) ) ) |
| 3 | wl-luk-pm2.04 | ⊢ ( ( 𝜂 → ( 𝜓 → 𝜑 ) ) → ( 𝜓 → ( 𝜂 → 𝜑 ) ) ) | |
| 4 | 2 3 | wl-impchain-mp-2 | ⊢ ( 𝜒 → ( 𝜃 → ( 𝜓 → ( 𝜂 → 𝜑 ) ) ) ) |
| 5 | 4 | wl-impchain-com-1.3 | ⊢ ( 𝜓 → ( 𝜃 → ( 𝜒 → ( 𝜂 → 𝜑 ) ) ) ) |