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Theorem sbcom3 2240
 Description: Substituting for and then for is equivalent to substituting for both and . (Contributed by Giovanni Mascellani, 8-Apr-2018.) Remove dependency on ax-11 1920. (Revised by Wolf Lammen, 16-Sep-2018.) (Proof shortened by Wolf Lammen, 16-Sep-2018.)
Assertion
Ref Expression
sbcom3

Proof of Theorem sbcom3
StepHypRef Expression
1 nfa1 1979 . . 3
2 drsb2 2207 . . 3
31, 2sbbid 2232 . 2
4 sb4b 2188 . . . 4
5 sbequ 2205 . . . . . 6
65pm5.74i 249 . . . . 5
76albii 1691 . . . 4
84, 7syl6bb 265 . . 3
9 sb4b 2188 . . 3
108, 9bitr4d 260 . 2
113, 10pm2.61i 168 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188  wal 1442  wsb 1797 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933  ax-13 2091 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ex 1664  df-nf 1668  df-sb 1798 This theorem is referenced by:  sbco  2241  sbidm  2243  sbcom  2247  equsb3  2261  wl-equsb3  31884
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