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Theorem sbal2 2211
 Description: Move quantifier in and out of substitution. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
sbal2
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbal2
StepHypRef Expression
1 alcom 1752 . . 3
2 nfnae 2044 . . . 4
3 nfnae 2044 . . . . . 6
4 dveeq1 2021 . . . . . 6
53, 4nfd 1782 . . . . 5
6 19.21t 1813 . . . . 5
75, 6syl 16 . . . 4
82, 7albid 1788 . . 3
91, 8syl5rbbr 252 . 2
10 sb6 2175 . 2
11 sb6 2175 . . 3
1211albii 1575 . 2
139, 10, 123bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wnf 1553  wsb 1658 This theorem is referenced by:  2sb5ndVD  29022  2sb5ndALT  29044 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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