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Theorem spimed 1601
Description: Deduction version of spime 1602. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 19-Feb-2018.)
Hypotheses
Ref Expression
spimed.1 (χ → Ⅎxφ)
spimed.2 (x = y → (φψ))
Assertion
Ref Expression
spimed (χ → (φxψ))

Proof of Theorem spimed
StepHypRef Expression
1 spimed.1 . . 3 (χ → Ⅎxφ)
21nfrd 1386 . 2 (χ → (φxφ))
3 a9e 1559 . . . 4 x x = y
4 spimed.2 . . . 4 (x = y → (φψ))
53, 4eximii 1466 . . 3 x(φψ)
6519.35i 1489 . 2 (xφxψ)
72, 6syl6 29 1 (χ → (φxψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1221  wnf 1322  wex 1354
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 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-i9 1396  ax-ial 1400
This theorem depends on definitions:  df-bi 110  df-nf 1323
This theorem is referenced by:  spime  1602
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