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Mirrors > Home > ILE Home > Th. List > com4t | GIF version |
Description: Commutation of antecedents. Rotate twice. (Contributed by NM, 25-Apr-1994.) |
Ref | Expression |
---|---|
com4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
com4t | ⊢ (𝜒 → (𝜃 → (𝜑 → (𝜓 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | com4l 84 | . 2 ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜏)))) |
3 | 2 | com4l 84 | 1 ⊢ (𝜒 → (𝜃 → (𝜑 → (𝜓 → 𝜏)))) |
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: com4r 86 com24 87 mopick 2091 tfri3 6327 |
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