Theorem 3pm3.2i 1177

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 982	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6	3, 4, 5	mpbir2an 944	1 |- ( ph /\ ps /\ ch )

Syntax hints:   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  mpbir3an  1181  3jaoi  1314  ftp  5750  4bc2eq6  10885  halfleoddlt  12078  strleun  12809  strle1g  12811  slotstnscsi  12899  slotsdnscsi  12927  slotsdifunifndx  12936  2irrexpqap  15322  lgslem2  15350  lgsdir2lem2  15378  lgsdir2lem3  15379  ex-dvds  15484  nconstwlpolem0  15820