Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-syl | Structured version Visualization version GIF version |
Description: An inference version of the transitive laws for implication luk-1 1662. Copy of syl 17 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-syl.1 | ⊢ (𝜑 → 𝜓) |
wl-luk-syl.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
wl-luk-syl | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-syl.2 | . 2 ⊢ (𝜓 → 𝜒) | |
2 | wl-luk-syl.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
3 | 2 | wl-luk-imim1i 35237 | . 2 ⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒)) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ (𝜑 → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 35233 |
This theorem is referenced by: wl-luk-imtrid 35239 wl-luk-pm2.18d 35240 wl-luk-imtrdi 35246 wl-luk-ax1 35248 wl-luk-pm2.27 35249 wl-luk-a1d 35255 wl-luk-id 35257 |
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