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Theorem sb3an 1829
Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 14-Dec-2006.)
Assertion
Ref Expression
sb3an

Proof of Theorem sb3an
StepHypRef Expression
1 df-3an 886 . . 3
21sbbii 1645 . 2
3 sban 1826 . 2
4 sban 1826 . . . 4
54anbi1i 431 . . 3
6 df-3an 886 . . 3
75, 6bitr4i 176 . 2
82, 3, 73bitri 195 1
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   w3a 884  wsb 1642
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-3an 886  df-nf 1347  df-sb 1643
This theorem is referenced by:  sbc3ang  2814
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