Theorem opreqi 3980

Description: Equality inference for operation value.

Hypothesis

Ref	Expression
opreq1i.1	|- A = B

Assertion

Ref	Expression
opreqi	|- (CAD) = (CBD)

Proof of Theorem opreqi

Step	Hyp	Ref	Expression
1		opreq1i.1	. 2 |- A = B
2		opreq 3973	. 2 |- (A = B -> (CAD) = (CBD))
3	1, 2	ax-mp 7	1 |- (CAD) = (CBD)

Syntax hints:   = wceq 958  (class class class)co 3969

This theorem is referenced by:  oprabval2gf 4032  cncfmet 7902  issubgi 8118  ghgrpilem1 8129  nvm 8258  shftefif1olem 8736  symgoprval 10399  cayleylem2 10405  subsp 10540

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-sep 2708  ax-pow 2748  ax-pr 2785

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-v 1815  df-dif 2052  df-un 2053  df-in 2054  df-ss 2056  df-nul 2284  df-pw 2406  df-sn 2416  df-pr 2417  df-op 2420  df-uni 2508  df-br 2625  df-opab 2672  df-cnv 3192  df-dm 3194  df-rn 3195  df-res 3196  df-ima 3197  df-fv 3204  df-opr 3971

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