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Theorem bnj121 29142
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj121.1
bnj121.2
bnj121.3
bnj121.4
Assertion
Ref Expression
bnj121
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,)   (,)   (,,)   (,,)   (,,)

Proof of Theorem bnj121
StepHypRef Expression
1 bnj121.1 . . 3
21sbcbii 3208 . 2
3 bnj121.2 . 2
4 bnj105 28990 . . . . . . . 8
54bnj90 28988 . . . . . . 7
65bicomi 194 . . . . . 6
7 bnj121.3 . . . . . 6
8 bnj121.4 . . . . . 6
96, 7, 83anbi123i 1142 . . . . 5
10 sbc3ang 3211 . . . . . 6
114, 10ax-mp 8 . . . . 5
129, 11bitr4i 244 . . . 4
1312imbi2i 304 . . 3
14 nfv 1629 . . . . 5
1514sbc19.21g 3217 . . . 4
164, 15ax-mp 8 . . 3
1713, 16bitr4i 244 . 2
182, 3, 173bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wcel 1725  cvv 2948  wsbc 3153   wfn 5441  c1o 6709   w-bnj15 28957 This theorem is referenced by:  bnj150  29148  bnj153  29152 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793  df-sn 3812  df-suc 4579  df-fn 5449  df-1o 6716
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