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 )

This proof depends on syntax axioms:   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  mpbir3an  1210  3jaoi  1344  ftp  5903  4bc2eq6  11234  halfleoddlt  12685  ballotfilemonn  13278  strleun  13516  strle1g  13518  slotstnscsi  13607  slotsdnscsi  13635  slotsdifunifndx  13644  2irrexpqap  16231  lgslem2  16342  lgsdir2lem2  16370  lgsdir2lem3  16371  usgrexmpldifpr  16712  0grsubgr  16727  konigsberglem4  16954  konigsberglem5  16955  ex-dvds  16966  nconstwlpolem0  17337