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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