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Theorem ifeq2 3667
 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 2853 . . 3
21uneq2d 3418 . 2
3 dfif6 3665 . 2
4 dfif6 3665 . 2
52, 3, 43eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1642  crab 2618   cun 3207  cif 3662 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 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-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-if 3663 This theorem is referenced by:  ifeq12  3675  ifeq2d  3677  ifbieq2i  3681  ifexg  3721
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