Theorem 19.34 1695

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 1649	. . 3 |- ( A. x ph -> E. x ph )
2	1	orim1i 761	. 2 |- ( ( A. x ph \/ E. x ps ) -> ( E. x ph \/ E. x ps ) )
3		19.43 1639	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
4	2, 3	sylibr 134	1 |- ( ( A. x ph \/ E. x ps ) -> E. x ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 709   A.wal 1362   E.wex 1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)