Theorem 3jaodd 31595

Description: Double deduction form of 3jaoi 1391. (Contributed by Scott Fenton, 20-Apr-2011.)

Hypotheses

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

Assertion

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

Proof of Theorem 3jaodd

Step	Hyp	Ref	Expression
1		3jaodd.1	. . . 4 |- ( ph -> ( ps -> ( ch -> et ) ) )
2	1	com3r 87	. . 3 |- ( ch -> ( ph -> ( ps -> et ) ) )
3		3jaodd.2	. . . 4 |- ( ph -> ( ps -> ( th -> et ) ) )
4	3	com3r 87	. . 3 |- ( th -> ( ph -> ( ps -> et ) ) )
5		3jaodd.3	. . . 4 |- ( ph -> ( ps -> ( ta -> et ) ) )
6	5	com3r 87	. . 3 |- ( ta -> ( ph -> ( ps -> et ) ) )
7	2, 4, 6	3jaoi 1391	. 2 |- ( ( ch \/ th \/ ta ) -> ( ph -> ( ps -> et ) ) )
8	7	com3l 89	1 |- ( ph -> ( ps -> ( ( ch \/ th \/ ta ) -> et ) ) )

Syntax hints:   -> wi 4   \/ w3o 1036

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 197  df-or 385  df-an 386  df-3or 1038  df-3an 1039

This theorem is referenced by: (None)