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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-impchain-mp-1 | Structured version Visualization version GIF version |
Description: This theorem is in fact a copy of wl-luk-syl 35238, and repeated here to demonstrate a recursive proof scheme. The number '1' in the theorem name indicates that a chain of length 1 is modified. (Contributed by Wolf Lammen, 6-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-impchain-mp-1.a | ⊢ (𝜒 → 𝜓) |
wl-impchain-mp-1.b | ⊢ (𝜓 → 𝜑) |
Ref | Expression |
---|---|
wl-impchain-mp-1 | ⊢ (𝜒 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-impchain-mp-1.a | . 2 ⊢ (𝜒 → 𝜓) | |
2 | wl-impchain-mp-1.b | . . 3 ⊢ (𝜓 → 𝜑) | |
3 | 2 | wl-luk-imim2i 35245 | . 2 ⊢ ((𝜒 → 𝜓) → (𝜒 → 𝜑)) |
4 | 1, 3 | wl-impchain-mp-0 35262 | 1 ⊢ (𝜒 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35233 ax-luk2 35234 ax-luk3 35235 |
This theorem is referenced by: wl-impchain-mp-2 35264 wl-impchain-com-1.3 35268 |
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