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Theorem chvar 1637
Description: Implicit substitution of y for x into a theorem. (Contributed by Raph Levien, 9-Jul-2003.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
chvar.1 xψ
chvar.2 (x = y → (φψ))
chvar.3 φ
Assertion
Ref Expression
chvar ψ

Proof of Theorem chvar
StepHypRef Expression
1 chvar.1 . . 3 xψ
2 chvar.2 . . . 4 (x = y → (φψ))
32biimpd 132 . . 3 (x = y → (φψ))
41, 3spim 1623 . 2 (xφψ)
5 chvar.3 . 2 φ
64, 5mpg 1337 1 ψ
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  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:  csbhypf  2879  opelopabsb  3988  findes  4269  fvmptssdm  5198  dfoprab4f  5761  dom2lem  6188  uzind4s  8289
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