Theorem dp2eq2i 29583

Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.)

Hypothesis

Ref	Expression
dp2eq1i.1	|- A = B

Assertion

Ref	Expression
dp2eq2i	|- _ C A = _ C B

Proof of Theorem dp2eq2i

Step	Hyp	Ref	Expression
1		dp2eq1i.1	. 2 |- A = B
2		dp2eq2 29581	. 2 |- ( A = B -> _ C A = _ C B )
3	1, 2	ax-mp 5	1 |- _ C A = _ C B

Syntax hints:   = wceq 1483  _cdp2 29577

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-uni 4437  df-br 4654  df-iota 5851  df-fv 5896  df-ov 6653  df-dp2 29578

This theorem is referenced by:  dp2eq12i  29584  hgt750lem2  30730