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Mirrors > Home > ILE Home > Th. List > expdcom | GIF version |
Description: Commuted form of expd 255. (Contributed by Alan Sare, 18-Mar-2012.) |
Ref | Expression |
---|---|
expdcom.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Ref | Expression |
---|---|
expdcom | ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expdcom.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
2 | 1 | expd 255 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | com3l 81 | 1 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 107 |
This theorem is referenced by: nndi 6287 nnmass 6288 mulexp 10125 expadd 10128 expmul 10131 |
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