Theorem 19.34 1619

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 1574	. . 3 |- ( A. x ph -> E. x ph )
2	1	orim1i 712	. 2 |- ( ( A. x ph \/ E. x ps ) -> ( E. x ph \/ E. x ps ) )
3		19.43 1564	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
4	2, 3	sylibr 132	1 |- ( ( A. x ph \/ E. x ps ) -> E. x ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 664   A.wal 1287   E.wex 1426

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)