Theorem 3pm3.2i 1081

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 257	. 2 |- (ph /\ ps)
4		3pm3.2i.3	. 2 |- ch
5		df-3an 886	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
6	3, 4, 5	mpbir2an 848	1 |- (ph /\ ps /\ ch)

Syntax hints:   /\ wa 97   /\ w3a 884

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 886

This theorem is referenced by:  mpbir3an  1085  3jaoi  1197  ftp  5291