Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-imtrdi | Structured version Visualization version GIF version |
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 35 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-imtrdi.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
wl-luk-imtrdi.2 | ⊢ (𝜒 → 𝜃) |
Ref | Expression |
---|---|
wl-luk-imtrdi | ⊢ (𝜑 → (𝜓 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-imtrdi.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | wl-luk-imtrdi.2 | . . 3 ⊢ (𝜒 → 𝜃) | |
3 | 2 | wl-luk-imim2i 35366 | . 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜃)) |
4 | 1, 3 | wl-luk-syl 35359 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35354 ax-luk2 35355 ax-luk3 35356 |
This theorem is referenced by: wl-luk-ax3 35368 wl-luk-pm2.27 35370 |
Copyright terms: Public domain | W3C validator |