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Theorem speiv 1739
Description: Inference from existential specialization, using implicit substitition. (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 147 . . 3 (x = y → (ψφ))
43spimev 1738 . 2 (ψxφ)
51, 4ax-mp 7 1 xφ
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347
This theorem is referenced by: (None)
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