Theorem exintr 1313

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 1188	. 2 |- (A.x(ph -> ps) -> A.xA.x(ph -> ps))
2		ancl 316	. . 3 |- ((ph -> ps) -> (ph -> (ph /\ ps)))
3	2	a4s 1168	. 2 |- (A.x(ph -> ps) -> (ph -> (ph /\ ps)))
4	1, 3	eximd 1248	1 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))

Syntax hints:   -> wi 3   /\ wa 239  A.wal 1134  E.wex 1164

This theorem is referenced by:  ceqsex 2157  r19.2z 2782  pwpw0 2956  pwsnALT 2995  bnj159 12276  bnj1024 12671  ceqsex3OLD 15931

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1143  ax-4 1157  ax-5o 1159

This theorem depends on definitions:  df-bi 163  df-an 241  df-ex 1165

Copyright terms: Public domain