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Theorem sbi1 2133
Description: Removal of implication from substitution. (Contributed by NM, 14-May-1993.)
Assertion
Ref Expression
sbi1

Proof of Theorem sbi1
StepHypRef Expression
1 sbequ2 1741 . . . . 5
2 sbequ2 1741 . . . . 5
31, 2syl5d 67 . . . 4
4 sbequ1 1991 . . . 4
53, 4syl6d 69 . . 3
65sps 1865 . 2
7 sb4 2097 . . 3
8 sb4 2097 . . . 4
9 ax-2 7 . . . . . 6
109al2imi 1636 . . . . 5
11 sb2 2093 . . . . 5
1210, 11syl6 33 . . . 4
138, 12syl6 33 . . 3
147, 13syl5d 67 . 2
156, 14pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  [wsb 1739
This theorem is referenced by:  spsbim  2135  sbim  2136  2sb5ndVD  33710  2sb5ndALT  33732
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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