Theorem 3anim123i 1137

Description: Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994.)

Hypotheses

Ref	Expression
3anim123i.1	|- (ph -> ps)
3anim123i.2	|- (ch -> th)
3anim123i.3	|- (ta -> et)

Assertion

Ref	Expression
3anim123i	|- ((ph /\ ch /\ ta) -> (ps /\ th /\ et))

Proof of Theorem 3anim123i

Step	Hyp	Ref	Expression
1		3anim123i.1	. . 3 |- (ph -> ps)
2	1	3ad2ant1 976	. 2 |- ((ph /\ ch /\ ta) -> ps)
3		3anim123i.2	. . 3 |- (ch -> th)
4	3	3ad2ant2 977	. 2 |- ((ph /\ ch /\ ta) -> th)
5		3anim123i.3	. . 3 |- (ta -> et)
6	5	3ad2ant3 978	. 2 |- ((ph /\ ch /\ ta) -> et)
7	2, 4, 6	3jca 1132	1 |- ((ph /\ ch /\ ta) -> (ps /\ th /\ et))

Syntax hints:   -> wi 4   /\ 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:  3anim1i  1138  3anim3i  1139  syl3an  1224  syl3anl  1233  spc3egv  2944