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  5834  4bc2eq6  11026  halfleoddlt  12445  strleun  13177  strle1g  13179  slotstnscsi  13268  slotsdnscsi  13296  slotsdifunifndx  13305  2irrexpqap  15692  lgslem2  15720  lgsdir2lem2  15748  lgsdir2lem3  15749  usgrexmpldifpr  16088  ex-dvds  16262  nconstwlpolem0  16603