Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-mps | Structured version Visualization version GIF version |
Description: Replacing a nested consequent. A sort of modus ponens in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
wl-mps.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
wl-mps.2 | ⊢ ((𝜑 → 𝜒) → 𝜃) |
Ref | Expression |
---|---|
wl-mps | ⊢ ((𝜑 → 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-mps.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | a2i 14 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒)) |
3 | wl-mps.2 | . 2 ⊢ ((𝜑 → 𝜒) → 𝜃) | |
4 | 2, 3 | syl 17 | 1 ⊢ ((𝜑 → 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: wl-syls1 35404 |
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