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Metamath Proof Explorer

Theorem 3jaobOLD

Description: Obsolete version of 3jaob as of 29-Jun-2025. (Contributed by NM, 13-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 3jaobOLD 
|- ( ( ( ph \/ ch \/ th ) -> ps ) <-> ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) )

Proof

Step Hyp Ref Expression
1 3mix1 
 |-  ( ph -> ( ph \/ ch \/ th ) )
2 1 imim1i 
 |-  ( ( ( ph \/ ch \/ th ) -> ps ) -> ( ph -> ps ) )
3 3mix2 
 |-  ( ch -> ( ph \/ ch \/ th ) )
4 3 imim1i 
 |-  ( ( ( ph \/ ch \/ th ) -> ps ) -> ( ch -> ps ) )
5 3mix3 
 |-  ( th -> ( ph \/ ch \/ th ) )
6 5 imim1i 
 |-  ( ( ( ph \/ ch \/ th ) -> ps ) -> ( th -> ps ) )
7 2 4 6 3jca 
 |-  ( ( ( ph \/ ch \/ th ) -> ps ) -> ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) )
8 3jao 
 |-  ( ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) -> ( ( ph \/ ch \/ th ) -> ps ) )
9 7 8 impbii 
 |-  ( ( ( ph \/ ch \/ th ) -> ps ) <-> ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) )