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Theorem sbco2h 1938
 Description: A composition law for substitution. (Contributed by NM, 30-Jun-1994.) (Proof rewritten by Jim Kingdon, 19-Mar-2018.)
Hypothesis
Ref Expression
sbco2h.1
Assertion
Ref Expression
sbco2h

Proof of Theorem sbco2h
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbco2h.1 . . . . 5
21nfi 1439 . . . 4
32sbco2yz 1937 . . 3
43sbbii 1739 . 2
5 nfv 1509 . . 3
65sbco2yz 1937 . 2
7 nfv 1509 . . 3
87sbco2yz 1937 . 2
94, 6, 83bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330  wsb 1736 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737 This theorem is referenced by:  sbco2  1939  sbco2d  1940  sbco3  1948  elsb3  1952  elsb4  1953  sb9  1955
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