Theorem exintr 1645

Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993.)

Assertion

Ref	Expression
exintr	|- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ( ph /\ ps ) ) )

Proof of Theorem exintr

Step	Hyp	Ref	Expression
1		exintrbi 1644	. 2 |- ( A. x ( ph -> ps ) -> ( E. x ph <-> E. x ( ph /\ ps ) ) )
2	1	biimpd 144	1 |- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ( ph /\ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 104   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-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:  ceqsex  2798  r19.2m  3533  r19.2mOLD  3534