Theorem 3pm3.2i 1202

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 1007	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6	3, 4, 5	mpbir2an 951	1 |- ( ph /\ ps /\ ch )

Syntax hints:   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  mpbir3an  1206  3jaoi  1340  ftp  5847  4bc2eq6  11082  halfleoddlt  12518  strleun  13250  strle1g  13252  slotstnscsi  13341  slotsdnscsi  13369  slotsdifunifndx  13378  2irrexpqap  15772  lgslem2  15803  lgsdir2lem2  15831  lgsdir2lem3  15832  usgrexmpldifpr  16173  0grsubgr  16188  konigsberglem4  16415  konigsberglem5  16416  ex-dvds  16427  nconstwlpolem0  16779