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Theorem brtcfn 6246
 Description: Binary relationship form of the stratified T-raising function. (Contributed by SF, 18-Mar-2015.)
Hypothesis
Ref Expression
brtcfn.1
Assertion
Ref Expression
brtcfn TcFn Tc

Proof of Theorem brtcfn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 brtcfn.1 . . . . 5
21snel1c 4140 . . . 4 1c
3 unieq 3900 . . . . . . 7
41unisn 3907 . . . . . . 7
53, 4syl6eq 2401 . . . . . 6
6 tceq 6158 . . . . . 6 Tc Tc
75, 6syl 15 . . . . 5 Tc Tc
8 df-tcfn 6107 . . . . 5 TcFn 1c Tc
9 tcex 6157 . . . . 5 Tc
107, 8, 9fvmpt 5700 . . . 4 1c TcFn Tc
112, 10ax-mp 8 . . 3 TcFn Tc
1211eqeq1i 2360 . 2 TcFn Tc
13 fntcfn 6245 . . 3 TcFn 1c
14 fnbrfvb 5358 . . 3 TcFn 1c 1c TcFn TcFn
1513, 2, 14mp2an 653 . 2 TcFn TcFn
16 eqcom 2355 . 2 Tc Tc
1712, 15, 163bitr3i 266 1 TcFn Tc
 Colors of variables: wff setvar class Syntax hints:   wb 176   wceq 1642   wcel 1710  cvv 2859  csn 3737  cuni 3891  1cc1c 4134   class class class wbr 4639   wfn 4776  cfv 4781   Tc ctc 6093  TcFnctcfn 6097 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-1c 4081  ax-sset 4082  ax-si 4083  ax-ins2 4084  ax-ins3 4085  ax-typlower 4086  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-reu 2621  df-rmo 2622  df-rab 2623  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-pss 3261  df-nul 3551  df-if 3663  df-pw 3724  df-sn 3741  df-pr 3742  df-uni 3892  df-int 3927  df-opk 4058  df-1c 4136  df-pw1 4137  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190  df-p6 4191  df-sik 4192  df-ssetk 4193  df-imagek 4194  df-idk 4195  df-iota 4339  df-0c 4377  df-addc 4378  df-nnc 4379  df-fin 4380  df-lefin 4440  df-ltfin 4441  df-ncfin 4442  df-tfin 4443  df-evenfin 4444  df-oddfin 4445  df-sfin 4446  df-spfin 4447  df-phi 4565  df-op 4566  df-proj1 4567  df-proj2 4568  df-opab 4623  df-br 4640  df-co 4726  df-ima 4727  df-id 4767  df-cnv 4785  df-rn 4786  df-dm 4787  df-fun 4789  df-fn 4790  df-fv 4795  df-mpt 5652  df-tc 6103  df-tcfn 6107 This theorem is referenced by:  nmembers1lem1  6268  nchoicelem11  6299  nchoicelem16  6304
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