Theorem 19.34 1675

Description: Theorem 19.34 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem 19.34

Step	Hyp	Ref	Expression
1		19.2 1672	. . 3 |- ( A. x ph -> E. x ph )
2	1	orim1i 505	. 2 |- ( ( A. x ph \/ E. x ps ) -> ( E. x ph \/ E. x ps ) )
3		19.43 1593	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
4	2, 3	sylibr 205	1 |- ( ( A. x ph \/ E. x ps ) -> E. x ( ph \/ ps ) )

Syntax hints:   -> wi 6   \/ wo 359   A.wal 1528   E.wex 1529

This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645

This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-fal 1313  df-ex 1530