Theorem 19.34 1674

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 1671	. . 3 |- ( A. x ph -> E. x ph )
2	1	orim1i 503	. 2 |- ( ( A. x ph \/ E. x ps ) -> ( E. x ph \/ E. x ps ) )
3		19.43 1592	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
4	2, 3	sylibr 203	1 |- ( ( A. x ph \/ E. x ps ) -> E. x ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 357   A.wal 1527   E.wex 1528

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529