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Theorem sbc19.21g 3227
 Description: Substitution for a variable not free in antecedent affects only the consequent. (Contributed by NM, 11-Oct-2004.)
Hypothesis
Ref Expression
sbcgf.1
Assertion
Ref Expression
sbc19.21g

Proof of Theorem sbc19.21g
StepHypRef Expression
1 sbcimg 3204 . 2
2 sbcgf.1 . . . 4
32sbcgf 3226 . . 3
43imbi1d 310 . 2
51, 4bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wnf 1554   wcel 1726  wsbc 3163 This theorem is referenced by:  bnj121  29315  bnj124  29316  bnj130  29319  bnj207  29326  bnj611  29363  bnj1000  29386 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164
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