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  5874  4bc2eq6  11162  halfleoddlt  12605  ballotfilemonn  13165  strleun  13401  strle1g  13403  slotstnscsi  13492  slotsdnscsi  13520  slotsdifunifndx  13529  2irrexpqap  15969  lgslem2  16000  lgsdir2lem2  16028  lgsdir2lem3  16029  usgrexmpldifpr  16370  0grsubgr  16385  konigsberglem4  16612  konigsberglem5  16613  ex-dvds  16624  nconstwlpolem0  16975