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Theorem sb5f 1682
 Description: Equivalence for substitution when y is not free in φ. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 18-May-2008.)
Hypothesis
Ref Expression
equs45f.1 (φyφ)
Assertion
Ref Expression
sb5f ([y / x]φx(x = y φ))

Proof of Theorem sb5f
StepHypRef Expression
1 equs45f.1 . . 3 (φyφ)
21sb6f 1681 . 2 ([y / x]φx(x = yφ))
31equs45f 1680 . 2 (x(x = y φ) ↔ x(x = yφ))
42, 3bitr4i 176 1 ([y / x]φx(x = y φ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∀wal 1240  ∃wex 1378  [wsb 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-11 1394  ax-4 1397  ax-i9 1420  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-sb 1643 This theorem is referenced by:  sbcof2  1688
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