Theorem 3jcad 1133

Description: Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)

Hypotheses

Ref	Expression
3jcad.1	|- (ph -> (ps -> ch))
3jcad.2	|- (ph -> (ps -> th))
3jcad.3	|- (ph -> (ps -> ta))

Assertion

Ref	Expression
3jcad	|- (ph -> (ps -> (ch /\ th /\ ta)))

Proof of Theorem 3jcad

Step	Hyp	Ref	Expression
1		3jcad.1	. . . 4 |- (ph -> (ps -> ch))
2	1	imp 418	. . 3 |- ((ph /\ ps) -> ch)
3		3jcad.2	. . . 4 |- (ph -> (ps -> th))
4	3	imp 418	. . 3 |- ((ph /\ ps) -> th)
5		3jcad.3	. . . 4 |- (ph -> (ps -> ta))
6	5	imp 418	. . 3 |- ((ph /\ ps) -> ta)
7	2, 4, 6	3jca 1132	. 2 |- ((ph /\ ps) -> (ch /\ th /\ ta))
8	7	ex 423	1 |- (ph -> (ps -> (ch /\ th /\ ta)))

Syntax hints:   -> wi 4   /\ 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: (None)