Theorem 3pm3.2i 1130

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

Hypotheses

Ref	Expression
3pm3.2i.1	⊢ φ
3pm3.2i.2	⊢ ψ
3pm3.2i.3	⊢ χ

Assertion

Ref	Expression
3pm3.2i	⊢ (φ ∧ ψ ∧ χ)

Proof of Theorem 3pm3.2i

Step	Hyp	Ref	Expression
1		3pm3.2i.1	. . 3 ⊢ φ
2		3pm3.2i.2	. . 3 ⊢ ψ
3	1, 2	pm3.2i 441	. 2 ⊢ (φ ∧ ψ)
4		3pm3.2i.3	. 2 ⊢ χ
5		df-3an 936	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ))
6	3, 4, 5	mpbir2an 886	1 ⊢ (φ ∧ ψ ∧ χ)

This proof depends on syntax axioms:   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by:  mpbir3an  1134  3jaoi  1245