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Theorem sbco 1839
Description: A composition law for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbco

Proof of Theorem sbco
StepHypRef Expression
1 equsb2 1666 . . 3
2 sbequ12 1651 . . . . 5
32bicomd 129 . . . 4
43sbimi 1644 . . 3
51, 4ax-mp 7 . 2
6 sbbi 1830 . 2
75, 6mpbi 133 1
Colors of variables: wff set class
Syntax hints:   wb 98  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-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:  sbco3v  1840
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