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Mirrors > Home > ILE Home > Th. List > com35 | GIF version |
Description: Commutation of antecedents. Swap 3rd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.) |
Ref | Expression |
---|---|
com5.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Ref | Expression |
---|---|
com35 | ⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | . . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) | |
2 | 1 | com34 83 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → (𝜏 → 𝜂))))) |
3 | 2 | com45 89 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜒 → 𝜂))))) |
4 | 3 | com34 83 | 1 ⊢ (𝜑 → (𝜓 → (𝜏 → (𝜃 → (𝜒 → 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: (None) |
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