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Theorem eucalgval2 13077
 Description: The value of the step function for Euclid's Algorithm on an ordered pair. (Contributed by Paul Chapman, 31-Mar-2011.) (Revised by Mario Carneiro, 28-May-2014.)
Hypothesis
Ref Expression
eucalgval.1
Assertion
Ref Expression
eucalgval2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem eucalgval2
StepHypRef Expression
1 simpr 449 . . . 4
21eqeq1d 2446 . . 3
3 opeq12 3988 . . 3
4 oveq12 6093 . . . 4
51, 4opeq12d 3994 . . 3
62, 3, 5ifbieq12d 3763 . 2
7 eucalgval.1 . 2
8 opex 4430 . . 3
9 opex 4430 . . 3
108, 9ifex 3799 . 2
116, 7, 10ovmpt2a 6207 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cif 3741  cop 3819  (class class class)co 6084   cmpt2 6086  cc0 8995  cn0 10226   cmo 11255 This theorem is referenced by:  eucalgval  13078 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-iota 5421  df-fun 5459  df-fv 5465  df-ov 6087  df-oprab 6088  df-mpt2 6089
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