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Theorem sbcom4 2162
 Description: Commutativity law for substitution. This theorem was incorrectly used as our previous version of pm11.07 2163 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:   ,,,   ,,
Allowed substitution hint:   ()

Proof of Theorem sbcom4
StepHypRef Expression
1 nfv 1674 . . . . 5
21sbf 2081 . . . 4
32sbbii 1709 . . 3
4 nfv 1674 . . . 4
54sbf 2081 . . 3
63, 5bitri 249 . 2
71sbf 2081 . . . 4
87sbbii 1709 . . 3
94sbf 2081 . . 3
108, 9bitri 249 . 2
116, 10bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184  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-12 1794  ax-13 1955 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703 This theorem is referenced by: (None)
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