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Mirrors > Home > MPE Home > Th. List > exp5c | Structured version Visualization version GIF version |
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.) |
Ref | Expression |
---|---|
exp5c.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))) |
Ref | Expression |
---|---|
exp5c | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp5c.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))) | |
2 | 1 | exp4a 435 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → (𝜏 → 𝜂)))) |
3 | 2 | expd 419 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: exp5l 450 fiint 8948 inf3lem2 9244 fgcl 22775 pclfinN 37651 hbtlem2 40652 |
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