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  11227  halfleoddlt  12677  ballotfilemonn  13270  strleun  13507  strle1g  13509  slotstnscsi  13598  slotsdnscsi  13626  slotsdifunifndx  13635  2irrexpqap  16133  lgslem2  16218  lgsdir2lem2  16246  lgsdir2lem3  16247  usgrexmpldifpr  16588  0grsubgr  16603  konigsberglem4  16830  konigsberglem5  16831  ex-dvds  16842  nconstwlpolem0  17211