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Theorem sbal 2204
 Description: Move universal quantifier in and out of substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbal
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbal
StepHypRef Expression
1 a16gb 2052 . . . . 5
21sbimi 1664 . . . 4
3 sbequ5 2124 . . . 4
4 sbbi 2141 . . . 4
52, 3, 43imtr3i 257 . . 3
6 a16gb 2052 . . 3
75, 6bitr3d 247 . 2
8 sbal1 2203 . 2
97, 8pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549  wsb 1658 This theorem is referenced by:  sbex  2205  sbalv  2206  sbcal  3208  sbcalg  3209 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-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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