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  11229  halfleoddlt  12680  ballotfilemonn  13273  strleun  13511  strle1g  13513  slotstnscsi  13602  slotsdnscsi  13630  slotsdifunifndx  13639  2irrexpqap  16175  lgslem2  16286  lgsdir2lem2  16314  lgsdir2lem3  16315  usgrexmpldifpr  16656  0grsubgr  16671  konigsberglem4  16898  konigsberglem5  16899  ex-dvds  16910  nconstwlpolem0  17280