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Theorem bnj538 29085
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj538.1
Assertion
Ref Expression
bnj538
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem bnj538
StepHypRef Expression
1 df-ral 2561 . . 3
2 bnj538.1 . . 3
31, 2bnj524 29082 . 2
4 sbcimg 3045 . . . . . 6
52, 4ax-mp 8 . . . . 5
62bnj525 29083 . . . . . 6
76imbi1i 315 . . . . 5
85, 7bitri 240 . . . 4
98albii 1556 . . 3
10 sbcalg 3052 . . . 4
112, 10ax-mp 8 . . 3
12 df-ral 2561 . . 3
139, 11, 123bitr4i 268 . 2
143, 13bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wcel 1696  wral 2556  cvv 2801  wsbc 3004 This theorem is referenced by:  bnj92  29210  bnj539  29239  bnj540  29240 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-sbc 3005
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