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Mirrors > Home > ILE Home > Th. List > com4l | GIF version |
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994.) (Proof shortened by O'Cat, 15-Aug-2004.) |
Ref | Expression |
---|---|
com4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
com4l | ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | com3l 75 | . 2 ⊢ (𝜓 → (𝜒 → (𝜑 → (𝜃 → 𝜏)))) |
3 | 2 | com34 77 | 1 ⊢ (𝜓 → (𝜒 → (𝜃 → (𝜑 → 𝜏)))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: com4t 79 com4r 80 com14 82 com5l 86 3impd 1118 |
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