Theorem 3pm3.2i 1130

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 441	. 2 |- (ph /\ ps)
4		3pm3.2i.3	. 2 |- ch
5		df-3an 936	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
6	3, 4, 5	mpbir2an 886	1 |- (ph /\ ps /\ ch)

Syntax hints:   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  mpbir3an  1134  3jaoi  1245