Theorem 19.45v 1913

Description: Version of 19.45 2107 with a dv condition, requiring fewer axioms. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
19.45v	|- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.45v

Step	Hyp	Ref	Expression
1		19.43 1810	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.9v 1896	. . 3 |- ( E. x ph <-> ph )
3	2	orbi1i 542	. 2 |- ( ( E. x ph \/ E. x ps ) <-> ( ph \/ E. x ps ) )
4	1, 3	bitri 264	1 |- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Syntax hints:   <-> wb 196   \/ wo 383   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705

This theorem is referenced by: (None)