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Theorem nfima 4619
Description: Bound-variable hypothesis builder for image. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypotheses
Ref Expression
nfima.1 xA
nfima.2 xB
Assertion
Ref Expression
nfima x(AB)

Proof of Theorem nfima
StepHypRef Expression
1 df-ima 4301 . 2 (AB) = ran (AB)
2 nfima.1 . . . 4 xA
3 nfima.2 . . . 4 xB
42, 3nfres 4557 . . 3 x(AB)
54nfrn 4522 . 2 xran (AB)
61, 5nfcxfr 2172 1 x(AB)
Colors of variables: wff set class
Syntax hints:  wnfc 2162  ran crn 4289  cres 4290  cima 4291
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-v 2553  df-un 2916  df-in 2918  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-xp 4294  df-cnv 4296  df-dm 4298  df-rn 4299  df-res 4300  df-ima 4301
This theorem is referenced by:  nfimad  4620  csbima12g  4629
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