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Theorem sbal2 2134
 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 1737 . . 3
2 nfnae 1956 . . . 4
3 nfnae 1956 . . . . . 6
4 dveeq1 2018 . . . . . 6
53, 4nfd 1766 . . . . 5
6 19.21t 1795 . . . . 5
75, 6syl 15 . . . 4
82, 7albid 1772 . . 3
91, 8syl5rbbr 251 . 2
10 sb6 2099 . 2
11 sb6 2099 . . 3
1211albii 1566 . 2
139, 10, 123bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wnf 1544  wsb 1648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by: (None)
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