Theorem exintr 793

Description: Introduce a conjunct in the scope of an existential quantifier.

Assertion

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

Proof of Theorem exintr

Step	Hyp	Ref	Expression
1		hba1 698	. 2 |- (A.x(ph -> ps) -> A.xA.x(ph -> ps))
2		ancl 242	. . 3 |- ((ph -> ps) -> (ph -> (ph /\ ps)))
3	2	a4s 682	. 2 |- (A.x(ph -> ps) -> (ph -> (ph /\ ps)))
4	1, 3	19.22d 744	1 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))

Syntax hints:   -> wi 2   /\ wa 196  A.wal 672  E.wex 678

This theorem is referenced by:  ceqsex 1370  r19.2z 1766  pwpw0 1883

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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