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Mirrors > Home > MPE Home > Th. List > an13s | Structured version Visualization version GIF version |
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.) |
Ref | Expression |
---|---|
an12s.1 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
Ref | Expression |
---|---|
an13s | ⊢ ((𝜒 ∧ (𝜓 ∧ 𝜑)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an12s.1 | . . . 4 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) | |
2 | 1 | exp32 421 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | com13 88 | . 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃))) |
4 | 3 | imp32 419 | 1 ⊢ ((𝜒 ∧ (𝜓 ∧ 𝜑)) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 |
This theorem is referenced by: cusgrfilem1 27818 abfmpeld 30985 |
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