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Theorem deceq2i 11337
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypothesis
Ref Expression
deceq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
deceq2i 𝐶𝐴 = 𝐶𝐵

Proof of Theorem deceq2i
StepHypRef Expression
1 deceq1i.1 . 2 𝐴 = 𝐵
2 deceq2 11334 . 2 (𝐴 = 𝐵𝐶𝐴 = 𝐶𝐵)
31, 2ax-mp 5 1 𝐶𝐴 = 𝐶𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  cdc 11325
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-rex 2901  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-br 4578  df-iota 5754  df-fv 5798  df-ov 6530  df-dec 11326
This theorem is referenced by:  deceq12i  11338
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