Theorem 3pm3.2i 1165

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 270	. 2 |- ( ph /\ ps )
4		3pm3.2i.3	. 2 |- ch
5		df-3an 970	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
6	3, 4, 5	mpbir2an 932	1 |- ( ph /\ ps /\ ch )

Syntax hints:   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  mpbir3an  1169  3jaoi  1293  ftp  5670  4bc2eq6  10687  halfleoddlt  11831  strleun  12484  strle1g  12485  2irrexpqap  13536  lgslem2  13542  lgsdir2lem2  13570  lgsdir2lem3  13571  ex-dvds  13611  nconstwlpolem0  13941