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  5900  4bc2eq6  11213  halfleoddlt  12661  ballotfilemonn  13221  strleun  13458  strle1g  13460  slotstnscsi  13549  slotsdnscsi  13577  slotsdifunifndx  13586  2irrexpqap  16080  lgslem2  16120  lgsdir2lem2  16148  lgsdir2lem3  16149  usgrexmpldifpr  16490  0grsubgr  16505  konigsberglem4  16732  konigsberglem5  16733  ex-dvds  16744  nconstwlpolem0  17113