Theorem 3pm3.2i 603

Description: Infer conjunction of premises.

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	. . . 4 ⊢ φ
2		3pm3.2i.2	. . . 4 ⊢ ψ
3	1, 2	pm3.2i 234	. . 3 ⊢ (φ ∧ ψ)
4		3pm3.2i.3	. . 3 ⊢ χ
5	3, 4	pm3.2i 234	. 2 ⊢ ((φ ∧ ψ) ∧ χ)
6		df-3an 583	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ))
7	5, 6	mpbir 165	1 ⊢ (φ ∧ ψ ∧ χ)

Syntax hints:   ∧ wa 196   ∧ w3a 581

This theorem is referenced by:  3jaoi 633  limon 2342  trcl 3489  mul0or 4210  divassz 4241  divdivdiv 4269  divdiv23z 4273  lemul2 4396  sqrlem6 4736  sqrlem20 4750  ruclem33 4917  projlem8 5200

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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