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Theorem sbco2d 2120
 Description: A composition law for substitution. (Contributed by NM, 2-Jun-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 1854 . . . 4
43sbco2 2118 . . 3
5 sbco2d.1 . . . . . 6
65sbrim 2095 . . . . 5
76sbbii 1709 . . . 4
81sbrim 2095 . . . 4
97, 8bitri 249 . . 3
105sbrim 2095 . . 3
114, 9, 103bitr3i 275 . 2
1211pm5.74ri 246 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wnf 1590  wsb 1702 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703 This theorem is referenced by:  sbco3  2121  sbco3OLD  2122
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