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Theorem spimeh 1605
Description: Existential introduction, using implicit substitition. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Revised by NM, 3-Feb-2015.) (New usage is discouraged.)
Hypotheses
Ref Expression
spimeh.1 (φxφ)
spimeh.2 (x = y → (φψ))
Assertion
Ref Expression
spimeh (φxψ)

Proof of Theorem spimeh
StepHypRef Expression
1 a9e 1564 . 2 x x = y
2 spimeh.1 . . 3 (φxφ)
3 spimeh.2 . . . 4 (x = y → (φψ))
43com12 27 . . 3 (φ → (x = yψ))
52, 4eximdh 1480 . 2 (φ → (x x = yxψ))
61, 5mpi 15 1 (φxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1224   = wceq 1226  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
This theorem is referenced by: (None)
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