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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-luk-imim2i | Structured version Visualization version GIF version |
Description: Inference adding common antecedents in an implication. Copy of imim2i 16 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-luk-imim2i.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
wl-luk-imim2i | ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-luk-imim2i.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | ax-luk1 36763 | . 2 ⊢ ((𝜒 → 𝜑) → ((𝜑 → 𝜓) → (𝜒 → 𝜓))) | |
3 | 1, 2 | wl-luk-mpi 36774 | 1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 36763 ax-luk2 36764 ax-luk3 36765 |
This theorem is referenced by: wl-luk-imtrdi 36776 wl-luk-ja 36783 wl-impchain-mp-1 36793 wl-impchain-mp-2 36794 |
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