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Mirrors > Home > ILE Home > Th. List > an31s | GIF version |
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.) |
Ref | Expression |
---|---|
an32s.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
an31s | ⊢ (((𝜒 ∧ 𝜓) ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an32s.1 | . . . 4 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
2 | 1 | exp31 362 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | com13 80 | . 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃))) |
4 | 3 | imp31 254 | 1 ⊢ (((𝜒 ∧ 𝜓) ∧ 𝜑) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem is referenced by: genpassl 7444 genpassu 7445 |
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