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Theorem sbco2h 1835
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 1348 . . . 4  F/
32sbco2yz 1834 . . 3
43sbbii 1645 . 2
5 nfv 1418 . . 3  F/
65sbco2yz 1834 . 2
7 nfv 1418 . . 3  F/
87sbco2yz 1834 . 2
94, 6, 83bitr3i 199 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240  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:  sbco2  1836  sbco2d  1837  sbco3  1845  elsb3  1849  elsb4  1850  sb9  1852
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