Theorem 3pm3.2i 603

Description: Infer conjunction of premises.

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	. . . 4 |- ph
2		3pm3.2i.2	. . . 4 |- ps
3	1, 2	pm3.2i 234	. . 3 |- (ph /\ ps)
4		3pm3.2i.3	. . 3 |- ch
5	3, 4	pm3.2i 234	. 2 |- ((ph /\ ps) /\ ch)
6		df-3an 583	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
7	5, 6	mpbir 165	1 |- (ph /\ ps /\ ch)

Syntax hints:   /\ wa 196   /\ w3a 581

This theorem is referenced by:  3jaoi 633  limon 2342  trcl 3489  mul0or 4210  divassz 4241  divdivdiv 4269  divdiv23z 4273  lemul2 4396  sqrlem6 4736  sqrlem20 4750  ruclem33 4917  projlem8 5200

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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