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Theorem sbi1 2119
 Description: Removal of implication from substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbi1

Proof of Theorem sbi1
StepHypRef Expression
1 sbequ2 1660 . . . . 5
2 sbequ2 1660 . . . . 5
31, 2syl5d 64 . . . 4
4 sbequ1 1943 . . . 4
53, 4syl6d 66 . . 3
65sps 1770 . 2
7 sb4 2089 . . 3
8 sb4 2089 . . . 4
9 ax-2 6 . . . . . 6
109al2imi 1570 . . . . 5
11 sb2 2086 . . . . 5
1210, 11syl6 31 . . . 4
138, 12syl6 31 . . 3
147, 13syl5d 64 . 2
156, 14pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549  wsb 1658 This theorem is referenced by:  sbim  2121  spsbim  2150  2sb5ndVD  28959  2sb5ndALT  28981 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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