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Theorem sbco2 1836
 Description: A composition law for substitution. (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sbco2.1 zφ
Assertion
Ref Expression
sbco2 ([y / z][z / x]φ ↔ [y / x]φ)

Proof of Theorem sbco2
StepHypRef Expression
1 sbco2.1 . . 3 zφ
21nfri 1409 . 2 (φzφ)
32sbco2h 1835 1 ([y / z][z / x]φ ↔ [y / x]φ)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98  Ⅎwnf 1346  [wsb 1642 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643 This theorem is referenced by:  nfsbt  1847  sb7af  1866  sbco4lem  1879  sbco4  1880  eqsb3  2138  clelsb3  2139  clelsb4  2140  sb8ab  2156  sbralie  2540  sbcco  2779
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