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Mirrors > Home > MPE Home > Th. List > 3imp231 | Structured version Visualization version GIF version |
Description: Importation inference. (Contributed by Alan Sare, 17-Oct-2017.) |
Ref | Expression |
---|---|
3imp.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
3imp231 | ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | com3l 89 | . 2 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃))) |
3 | 2 | 3imp 1112 | 1 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1088 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 398 df-3an 1090 |
This theorem is referenced by: 3imp21 1115 sotri2 6087 oawordri 8501 undifixp 8878 sslttr 27175 ssltun2 27177 ssltleft 27229 eel12131 43087 odd2prm2 46000 |
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