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  5869  4bc2eq6  11137  halfleoddlt  12580  ballotfilemonn  13140  strleun  13317  strle1g  13319  slotstnscsi  13408  slotsdnscsi  13436  slotsdifunifndx  13445  2irrexpqap  15843  lgslem2  15874  lgsdir2lem2  15902  lgsdir2lem3  15903  usgrexmpldifpr  16244  0grsubgr  16259  konigsberglem4  16486  konigsberglem5  16487  ex-dvds  16498  nconstwlpolem0  16849