Theorem exintr 1819

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 1818	. 2 |- ( A. x ( ph -> ps ) -> ( E. x ph <-> E. x ( ph /\ ps ) ) )
2	1	biimpd 219	1 |- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ( ph /\ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481   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

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  equs4v  1930  equs4  2290  eupickbi  2539  ceqsex  3241  r19.2z  4060  pwpw0  4344  pwsnALT  4429  bnj1023  30851  bnj1109  30857  pm10.55  38568