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Theorem exintr 1634
Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993.)
Assertion
Ref Expression
exintr (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))

Proof of Theorem exintr
StepHypRef Expression
1 exintrbi 1633 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
21biimpd 144 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wal 1351  wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  ceqsex  2775  r19.2m  3509  r19.2mOLD  3510
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