Theorem exintr 1614

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.xph -> E.x(ph /\ ps)))

Proof of Theorem exintr

Step	Hyp	Ref	Expression
1		exintrbi 1613	. 2 |- (A.x(ph -> ps) -> (E.xph <-> E.x(ph /\ ps)))
2	1	biimpd 198	1 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))

Syntax hints:   -> wi 4   /\ wa 358  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  ceqsex  2894  r19.2z  3640  pwpw0  3856  pwsnALT  3883