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Theorem sbco2 1888
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 1458 . 2 (𝜑 → ∀𝑧𝜑)
32sbco2h 1887 1 ([𝑦 / 𝑧][𝑧 / 𝑥]𝜑 ↔ [𝑦 / 𝑥]𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wnf 1395  [wsb 1693
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694
This theorem is referenced by:  nfsbt  1899  sb7af  1918  sbco4lem  1931  sbco4  1932  eqsb3  2192  clelsb3  2193  clelsb4  2194  sb8ab  2210  clelsb3f  2233  sbralie  2604  sbcco  2862
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