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Mirrors > Home > MPE Home > Th. List > Mathboxes > imp5p | Structured version Visualization version GIF version |
Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.) |
Ref | Expression |
---|---|
3imp5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
imp5p | ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜂))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp5.1 | . . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | 1 | com52l 102 | . . 3 ⊢ (𝜒 → (𝜃 → (𝜏 → (𝜑 → (𝜓 → 𝜂))))) |
3 | 2 | 3imp 1110 | . 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → (𝜑 → (𝜓 → 𝜂))) |
4 | 3 | com3l 89 | 1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜂))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1086 |
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 397 df-3an 1088 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |