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Theorem axie2 2329
Description: A key property of existential quantification (intuitionistic logic axiom ax-ie2). (Contributed by Jim Kingdon, 31-Dec-2017.)
Assertion
Ref Expression
axie2 (x(ψxψ) → (x(φψ) ↔ (xφψ)))

Proof of Theorem axie2
StepHypRef Expression
1 df-nf 1545 . 2 (Ⅎxψx(ψxψ))
2 19.23t 1800 . 2 (Ⅎxψ → (x(φψ) ↔ (xφψ)))
31, 2sylbir 204 1 (x(ψxψ) → (x(φψ) ↔ (xφψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  wex 1541  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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