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Theorem spimd 9174
Description: Deduction form of spim 1623. (Contributed by BJ, 17-Oct-2019.)
Hypotheses
Ref Expression
spimd.nf (φ → Ⅎxχ)
spimd.1 (φx(x = y → (ψχ)))
Assertion
Ref Expression
spimd (φ → (xψχ))

Proof of Theorem spimd
StepHypRef Expression
1 spimd.nf . 2 (φ → Ⅎxχ)
2 spimd.1 . 2 (φx(x = y → (ψχ)))
3 spimt 1621 . 2 ((Ⅎxχ x(x = y → (ψχ))) → (xψχ))
41, 2, 3syl2anc 391 1 (φ → (xψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346
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-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  2spim  9175
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