Theorem tfrlem3 7066

Description: Lemma for transfinite recursion. Let be the class of "acceptable" functions. The final thing we're interested in is the union of all these acceptable functions. This lemma just changes some bound variables in for later use. (Contributed by NM, 9-Apr-1995.)

Hypothesis

Ref	Expression
tfrlem3.1

Assertion

Ref	Expression
tfrlem3

Distinct variable groups:   ,   ,,,,,,

Proof of Theorem tfrlem3

Step	Hyp	Ref	Expression
1		tfrlem3.1	. . 3
2		vex 3112	. . 3
3	1, 2	tfrlem3a 7065	. 2
4	3	abbi2i 2590	1

Syntax hints:  /\wa 369  =wceq 1395  {cab 2442  A.wral 2807  E.wrex 2808  con0 4883  |`cres 5006  Fnwfn 5588  `cfv 5593

This theorem is referenced by:  tfrlem4  7067  tfrlem8  7072  rdglem1  7100

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-res 5016  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601