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Theorem dp2eq12i 30582
Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.)
Hypotheses
Ref Expression
dp2eq1i.1 𝐴 = 𝐵
dp2eq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
dp2eq12i 𝐴𝐶 = 𝐵𝐷

Proof of Theorem dp2eq12i
StepHypRef Expression
1 dp2eq1i.1 . . 3 𝐴 = 𝐵
21dp2eq1i 30580 . 2 𝐴𝐶 = 𝐵𝐶
3 dp2eq12i.2 . . 3 𝐶 = 𝐷
43dp2eq2i 30581 . 2 𝐵𝐶 = 𝐵𝐷
52, 4eqtri 2824 1 𝐴𝐶 = 𝐵𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  cdp2 30576
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-iota 6287  df-fv 6336  df-ov 7142  df-dp2 30577
This theorem is referenced by: (None)
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