Theorem 3pm3.2i 1199

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

Hypotheses

Ref	Expression
3pm3.2i.1	|- ph
3pm3.2i.2	|- ps
3pm3.2i.3	|- ch

Assertion

Ref	Expression
3pm3.2i	|- ( ph /\ ps /\ ch )

Proof of Theorem 3pm3.2i

Step	Hyp	Ref	Expression
1		3pm3.2i.1	. . 3 |- ph
2		3pm3.2i.2	. . 3 |- ps
3	1, 2	pm3.2i 272	. 2 |- ( ph /\ ps )
4		3pm3.2i.3	. 2 |- ch
5		df-3an 1004	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6	3, 4, 5	mpbir2an 948	1 |- ( ph /\ ps /\ ch )

Syntax hints:   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  mpbir3an  1203  3jaoi  1337  ftp  5832  4bc2eq6  11024  halfleoddlt  12442  strleun  13174  strle1g  13176  slotstnscsi  13265  slotsdnscsi  13293  slotsdifunifndx  13302  2irrexpqap  15689  lgslem2  15717  lgsdir2lem2  15745  lgsdir2lem3  15746  usgrexmpldifpr  16084  ex-dvds  16236  nconstwlpolem0  16577