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Mirrors > Home > ILE Home > Th. List > com45 | GIF version |
Description: Commutation of antecedents. Swap 4th and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.) |
Ref | Expression |
---|---|
com5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
com45 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | pm2.04 82 | . 2 ⊢ ((𝜃 → (𝜏 → 𝜂)) → (𝜏 → (𝜃 → 𝜂))) | |
3 | 1, 2 | syl8 71 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃 → 𝜂))))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: com35 90 com25 91 com5l 92 |
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