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Theorem speiv 2000
Description: Inference from existential specialization, using implicit substitution. (Contributed by NM, 19-Aug-1993.)
Hypotheses
Ref Expression
speiv.1 (x = y → (φψ))
speiv.2 ψ
Assertion
Ref Expression
speiv xφ
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem speiv
StepHypRef Expression
1 speiv.2 . 2 ψ
2 speiv.1 . . . 4 (x = y → (φψ))
32biimprd 214 . . 3 (x = y → (ψφ))
43spimev 1999 . 2 (ψxφ)
51, 4ax-mp 5 1 xφ
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wex 1541
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-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  ce0addcnnul  6179
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