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Theorem sb6f 2126
Description: Equivalence for substitution when is not free in . The implication "to the left" is sb2 2093 and does not require the non-freeness hypothesis. Theorem sb6 2173 replaces the non-freeness hypothesis with a dv condition. (Contributed by NM, 2-Jun-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sb6f.1
Assertion
Ref Expression
sb6f

Proof of Theorem sb6f
StepHypRef Expression
1 sb6f.1 . . . . 5
21nfri 1874 . . . 4
32sbimi 1745 . . 3
4 sb4a 1997 . . 3
53, 4syl 16 . 2
6 sb2 2093 . 2
75, 6impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sb5f  2127
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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