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Mirrors > Home > MPE Home > Th. List > exp5j | Structured version Visualization version GIF version |
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.) |
Ref | Expression |
---|---|
exp5j.1 | ⊢ (𝜑 → ((((𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)) |
Ref | Expression |
---|---|
exp5j | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp5j.1 | . . 3 ⊢ (𝜑 → ((((𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)) | |
2 | 1 | expd 451 | . 2 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → (𝜏 → 𝜂))) |
3 | 2 | exp4c 634 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: lcmfunsnlem2lem1 15189 exp510 31471 |
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