Theorem exintr 1117

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 1003	. 2 |- (A.x(ph -> ps) -> A.xA.x(ph -> ps))
2		ancl 294	. . 3 |- ((ph -> ps) -> (ph -> (ph /\ ps)))
3	2	a4s 984	. 2 |- (A.x(ph -> ps) -> (ph -> (ph /\ ps)))
4	1, 3	19.22d 1062	1 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 954  E.wex 980

This theorem is referenced by:  ceqsex 1834  r19.2z 2347  pwpw0 2469  pwsnALT 2501

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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