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Theorem spime 1607
Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Mar-2018.)
Hypotheses
Ref Expression
spime.1 xφ
spime.2 (x = y → (φψ))
Assertion
Ref Expression
spime (φxψ)

Proof of Theorem spime
StepHypRef Expression
1 spime.1 . . . 4 xφ
21a1i 9 . . 3 ( ⊤ → Ⅎxφ)
3 spime.2 . . 3 (x = y → (φψ))
42, 3spimed 1606 . 2 ( ⊤ → (φxψ))
54trud 1235 1 (φxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wtru 1227  wnf 1325  wex 1358
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-i9 1400  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326
This theorem is referenced by:  spimev  1719
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