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Theorem tcex 6158
Description: The cardinal T operation always yields a set. (Contributed by SF, 2-Mar-2015.)
Assertion
Ref Expression
tcex Tc

Proof of Theorem tcex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-tc 6104 . 2 Tc NC Nc 1
2 iotaex 4357 . 2 NC Nc 1
31, 2eqeltri 2423 1 Tc
Colors of variables: wff setvar class
Syntax hints:   wa 358   wceq 1642   wcel 1710  wrex 2616  cvv 2860  1 cpw1 4136  cio 4338   NC cncs 6089   Nc cnc 6092   Tc ctc 6094
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4079
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ne 2519  df-ral 2620  df-rex 2621  df-v 2862  df-sbc 3048  df-nin 3212  df-compl 3213  df-in 3214  df-un 3215  df-dif 3216  df-ss 3260  df-nul 3552  df-sn 3742  df-pr 3743  df-uni 3893  df-iota 4340  df-tc 6104
This theorem is referenced by:  fntcfn  6246  brtcfn  6247  nmembers1lem1  6269  nchoicelem11  6300  nchoicelem16  6305
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