Theorem 19.33-2 38581

Description: Theorem *11.421 in [WhiteheadRussell] p. 163. Theorem 19.33 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
19.33-2	|- ( ( A. x A. y ph \/ A. x A. y ps ) -> A. x A. y ( ph \/ ps ) )

Proof of Theorem 19.33-2

Step	Hyp	Ref	Expression
1		orc 400	. . 3 |- ( ph -> ( ph \/ ps ) )
2	1	2alimi 1740	. 2 |- ( A. x A. y ph -> A. x A. y ( ph \/ ps ) )
3		olc 399	. . 3 |- ( ps -> ( ph \/ ps ) )
4	3	2alimi 1740	. 2 |- ( A. x A. y ps -> A. x A. y ( ph \/ ps ) )
5	2, 4	jaoi 394	1 |- ( ( A. x A. y ph \/ A. x A. y ps ) -> A. x A. y ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 383   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by: (None)