Theorem exintrbi 1476

Description: Add/remove a conjunct in the scope of an existential quantifier. (Contributed by Raph Levien, 3-Jul-2006.)

Assertion

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

Proof of Theorem exintrbi

Step	Hyp	Ref	Expression
1		pm4.71 697	. . 3 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2	1	albii 1346	. 2 |- (A.x(ph -> ps) <-> A.x(ph <-> (ph /\ ps)))
3		exbi 1397	. 2 |- (A.x(ph <-> (ph /\ ps)) -> (E.xph <-> E.x(ph /\ ps)))
4	2, 3	sylbi 216	1 |- (A.x(ph -> ps) -> (E.xph <-> E.x(ph /\ ps)))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240  A.wal 1296  E.wex 1326

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327

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