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Theorem sbco2d 2164
 Description: A composition law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
sbco2d.1
sbco2d.2
sbco2d.3
Assertion
Ref Expression
sbco2d

Proof of Theorem sbco2d
StepHypRef Expression
1 sbco2d.2 . . . . 5
2 sbco2d.3 . . . . 5
31, 2nfim1 1831 . . . 4
43sbco2 2163 . . 3
5 sbco2d.1 . . . . . 6
65sbrim 2138 . . . . 5
76sbbii 1666 . . . 4
81sbrim 2138 . . . 4
97, 8bitri 242 . . 3
105sbrim 2138 . . 3
114, 9, 103bitr3i 268 . 2
1211pm5.74ri 239 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wnf 1554  wsb 1659 This theorem is referenced by:  sbco3  2165 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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