Theorem 19.33 1460

Description: Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem 19.33

Step	Hyp	Ref	Expression
1		orc 701	. . 3 |- ( ph -> ( ph \/ ps ) )
2	1	alimi 1431	. 2 |- ( A. x ph -> A. x ( ph \/ ps ) )
3		olc 700	. . 3 |- ( ps -> ( ph \/ ps ) )
4	3	alimi 1431	. 2 |- ( A. x ps -> A. x ( ph \/ ps ) )
5	2, 4	jaoi 705	1 |- ( ( A. x ph \/ A. x ps ) -> A. x ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 697   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-gen 1425

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.33b2  1608