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Theorem sbcom4 2190
 Description: Commutativity law for substitution. This theorem was incorrectly used as our previous version of pm11.07 2191 but may still be useful. (Contributed by Andrew Salmon, 17-Jun-2011.) (Proof shortened by Jim Kingdon, 22-Jan-2018.)
Assertion
Ref Expression
sbcom4
Distinct variable groups:   ,,,   ,,

Proof of Theorem sbcom4
StepHypRef Expression
1 nfv 1707 . . 3
21sbf 2121 . 2
3 nfv 1707 . . . 4
43sbf 2121 . . 3
54sbbii 1746 . 2
63sbf 2121 . . . 4
76sbbii 1746 . . 3
81sbf 2121 . . 3
97, 8bitri 249 . 2
102, 5, 93bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  [wsb 1739 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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