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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-impchain-a1-3 | Structured version Visualization version GIF version |
Description: Inference rule, a copy of a1dd 50. A recursive proof depending on previous instances, and demonstrating the proof pattern. (Contributed by Wolf Lammen, 20-Jun-2020.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-impchain-a1-3.a | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
wl-impchain-a1-3 | ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-impchain-a1-3.a | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | wl-impchain-a1-2 35144 | . 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜒))) |
3 | 2 | wl-impchain-com-2.3 35139 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35101 ax-luk2 35102 ax-luk3 35103 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |