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Theorem sbco2 1938
 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 1499 . 2 (𝜑 → ∀𝑧𝜑)
32sbco2h 1937 1 ([𝑦 / 𝑧][𝑧 / 𝑥]𝜑 ↔ [𝑦 / 𝑥]𝜑)
 Colors of variables: wff set class Syntax hints:   ↔ wb 104  Ⅎwnf 1436  [wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736 This theorem is referenced by:  nfsbt  1949  sb7af  1968  sbco4lem  1981  sbco4  1982  eqsb3  2243  clelsb3  2244  clelsb4  2245  sb8ab  2261  clelsb3f  2285  sbralie  2670  sbcco  2930
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