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Metamath Proof Explorer

Theorem 3pm3.2i

Description: Infer conjunction of premises. (Contributed by NM, 10-Feb-1995)

Ref Expression
Hypotheses 3pm3.2i.1 ⊢ 𝜑
3pm3.2i.2 ⊢ 𝜓
3pm3.2i.3 ⊢ 𝜒
Assertion 3pm3.2i ( 𝜑 ∧ 𝜓 ∧ 𝜒 )

Proof

Step Hyp Ref Expression
1 3pm3.2i.1 ⊢ 𝜑
2 3pm3.2i.2 ⊢ 𝜓
3 3pm3.2i.3 ⊢ 𝜒
4 1 2 pm3.2i ⊢ ( 𝜑 ∧ 𝜓 )
5 df-3an ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) )
6 4 3 5 mpbir2an ⊢ ( 𝜑 ∧ 𝜓 ∧ 𝜒 )