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Theorem tfr1a 6684
 Description: A weak version of tfr1 6687 which is useful for proofs that avoid the Axiom of Replacement. (Contributed by Mario Carneiro, 24-Jun-2015.)
Hypothesis
Ref Expression
tfr.1 recs
Assertion
Ref Expression
tfr1a

Proof of Theorem tfr1a
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2442 . . . 4
21tfrlem7 6673 . . 3 recs
3 tfr.1 . . . 4 recs
43funeqi 5503 . . 3 recs
52, 4mpbir 202 . 2
61tfrlem16 6683 . . 3 recs
73dmeqi 5100 . . . 4 recs
8 limeq 4622 . . . 4 recs recs
97, 8ax-mp 5 . . 3 recs
106, 9mpbir 202 . 2
115, 10pm3.2i 443 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653  cab 2428  wral 2711  wrex 2712  con0 4610   wlim 4611   cdm 4907   cres 4909   wfun 5477   wfn 5478  cfv 5483  recscrecs 6661 This theorem is referenced by:  tfr2b  6686  rdgfun  6703  rdgdmlim  6704  ordtypelem3  7518  ordtypelem4  7519  ordtypelem5  7520  ordtypelem6  7521  ordtypelem7  7522  ordtypelem9  7524 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-13 1729  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pow 4406  ax-pr 4432  ax-un 4730 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-reu 2718  df-rab 2720  df-v 2964  df-sbc 3168  df-csb 3268  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-pss 3322  df-nul 3614  df-if 3764  df-pw 3825  df-sn 3844  df-pr 3845  df-tp 3846  df-op 3847  df-uni 4040  df-iun 4119  df-br 4238  df-opab 4292  df-mpt 4293  df-tr 4328  df-eprel 4523  df-id 4527  df-po 4532  df-so 4533  df-fr 4570  df-we 4572  df-ord 4613  df-on 4614  df-lim 4615  df-suc 4616  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-rn 4918  df-res 4919  df-ima 4920  df-iota 5447  df-fun 5485  df-fn 5486  df-f 5487  df-f1 5488  df-fo 5489  df-f1o 5490  df-fv 5491  df-recs 6662
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