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Theorem sb5f 2184
 Description: Equivalence for substitution when is not free in . The implication "to the right" is sb1 1793 and does not require the non-freeness hypothesis. Theorem sb5 2229 replaces the non-freeness hypothesis with a dv condition. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sb6f.1
Assertion
Ref Expression
sb5f

Proof of Theorem sb5f
StepHypRef Expression
1 sb6f.1 . . 3
21sb6f 2183 . 2
31equs45f 2148 . 2
42, 3bitr4i 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435  wex 1657  wnf 1661  wsb 1790 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791 This theorem is referenced by:  sb7f  2252
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