Theorem 3pm3.2i 1206

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 1011	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6	3, 4, 5	mpbir2an 955	1 |- ( ph /\ ps /\ ch )

Syntax hints:   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  mpbir3an  1210  3jaoi  1344  ftp  5891  4bc2eq6  11191  halfleoddlt  12639  ballotfilemonn  13199  strleun  13435  strle1g  13437  slotstnscsi  13526  slotsdnscsi  13554  slotsdifunifndx  13563  2irrexpqap  16003  lgslem2  16034  lgsdir2lem2  16062  lgsdir2lem3  16063  usgrexmpldifpr  16404  0grsubgr  16419  konigsberglem4  16646  konigsberglem5  16647  ex-dvds  16658  nconstwlpolem0  17018