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Mirrors > Home > ILE Home > Th. List > exp53 | GIF version |
Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.) |
Ref | Expression |
---|---|
exp53.1 | ⊢ ((((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
exp53 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp53.1 | . . 3 ⊢ ((((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂) | |
2 | 1 | ex 114 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜃)) → (𝜏 → 𝜂)) |
3 | 2 | exp43 370 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: xpdom2 6776 elfzodifsumelfzo 10100 |
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