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Theorem ifeq12d 3408
 Description: Equality deduction for conditional operator. (Contributed by NM, 24-Mar-2015.)
Hypotheses
Ref Expression
ifeq1d.1
ifeq12d.2
Assertion
Ref Expression
ifeq12d

Proof of Theorem ifeq12d
StepHypRef Expression
1 ifeq1d.1 . . 3
21ifeq1d 3406 . 2
3 ifeq12d.2 . . 3
43ifeq2d 3407 . 2
52, 4eqtrd 2120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1289  cif 3391 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070 This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rab 2368  df-v 2621  df-un 3003  df-if 3392 This theorem is referenced by:  ifbieq12d  3415  exp3val  9945  eucalgval  11301
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