Theorem 19.34 1672

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 1626	. . 3 |- ( A. x ph -> E. x ph )
2	1	orim1i 750	. 2 |- ( ( A. x ph \/ E. x ps ) -> ( E. x ph \/ E. x ps ) )
3		19.43 1616	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
4	2, 3	sylibr 133	1 |- ( ( A. x ph \/ E. x ps ) -> E. x ( ph \/ ps ) )

Syntax hints:   -> wi 4   \/ wo 698   A.wal 1341   E.wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)