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Theorem ifeq2 3335
 Description: Equality theorem for conditional operator. (Contributed by NM, 1-Sep-2004.) (Revised by Mario Carneiro, 8-Sep-2013.)
Assertion
Ref Expression
ifeq2

Proof of Theorem ifeq2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rabeq 2551 . . 3
21uneq2d 3097 . 2
3 dfif6 3333 . 2
4 dfif6 3333 . 2
52, 3, 43eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1243  crab 2310   cun 2915  cif 3331 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-un 2922  df-if 3332 This theorem is referenced by:  ifeq12  3344  ifeq2d  3346  ifbieq2i  3351
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