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Theorem sbal2 1898
 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 1367 . . 3
2 hbnae 1609 . . . 4
3 dveeq1 1895 . . . . . . 7
43alimi 1344 . . . . . 6
54hbnaes 1611 . . . . 5
6 19.21ht 1473 . . . . 5
75, 6syl 14 . . . 4
82, 7albidh 1369 . . 3
91, 8syl5rbbr 184 . 2
10 sb6 1766 . 2
11 sb6 1766 . . 3
1211albii 1359 . 2
139, 10, 123bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98  wal 1241  wsb 1645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646 This theorem is referenced by: (None)
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