Theorem 3pm3.2i 1201

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 272	. 2 ⊢ (𝜑 ∧ 𝜓)
4		3pm3.2i.3	. 2 ⊢ 𝜒
5		df-3an 1006	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
6	3, 4, 5	mpbir2an 950	1 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Syntax hints:   ∧ wa 104   ∧ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  mpbir3an  1205  3jaoi  1339  ftp  5842  4bc2eq6  11042  halfleoddlt  12478  strleun  13210  strle1g  13212  slotstnscsi  13301  slotsdnscsi  13329  slotsdifunifndx  13338  2irrexpqap  15731  lgslem2  15759  lgsdir2lem2  15787  lgsdir2lem3  15788  usgrexmpldifpr  16129  0grsubgr  16144  konigsberglem4  16371  konigsberglem5  16372  ex-dvds  16383  nconstwlpolem0  16735