Metamath Proof Explorer

Theorem 19.33

Description: Theorem 19.33 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.33 
|- ( ( A. x ph \/ A. x ps ) -> A. x ( ph \/ ps ) )

Proof

Step Hyp Ref Expression
1 orc 
 |-  ( ph -> ( ph \/ ps ) )
2 1 alimi 
 |-  ( A. x ph -> A. x ( ph \/ ps ) )
3 olc 
 |-  ( ps -> ( ph \/ ps ) )
4 3 alimi 
 |-  ( A. x ps -> A. x ( ph \/ ps ) )
5 2 4 jaoi 
 |-  ( ( A. x ph \/ A. x ps ) -> A. x ( ph \/ ps ) )