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Theorem sbc19.21g 2907
 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 2880 . 2
2 sbcgf.1 . . . 4
32sbcgf 2906 . . 3
43imbi1d 229 . 2
51, 4bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wnf 1394   wcel 1438  wsbc 2840 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070 This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-sbc 2841 This theorem is referenced by: (None)
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