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Theorem oveq2 5531
 Description: Equality theorem for operation value. (Contributed by set.mm contributors, 28-Feb-1995.)
Assertion
Ref Expression
oveq2 (A = B → (CFA) = (CFB))

Proof of Theorem oveq2
StepHypRef Expression
1 opeq2 4579 . . 3 (A = BC, A = C, B)
21fveq2d 5332 . 2 (A = B → (FC, A) = (FC, B))
3 df-ov 5526 . 2 (CFA) = (FC, A)
4 df-ov 5526 . 2 (CFB) = (FC, B)
52, 3, 43eqtr4g 2410 1 (A = B → (CFA) = (CFB))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  ⟨cop 4561   ‘cfv 4781  (class class class)co 5525 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-1c 4081  ax-sset 4082  ax-si 4083  ax-ins2 4084  ax-ins3 4085  ax-typlower 4086  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-nul 3551  df-if 3663  df-pw 3724  df-sn 3741  df-pr 3742  df-uni 3892  df-int 3927  df-opk 4058  df-1c 4136  df-pw1 4137  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190  df-p6 4191  df-sik 4192  df-ssetk 4193  df-imagek 4194  df-idk 4195  df-iota 4339  df-addc 4378  df-nnc 4379  df-phi 4565  df-op 4566  df-br 4640  df-fv 4795  df-ov 5526 This theorem is referenced by:  oveq12  5532  oveq2i  5534  oveq2d  5538  rspceov  5556  fovcl  5588  ov3  5599  ndmovcl  5614  caovcld  5622  caovcomg  5624  caovassg  5626  caovcan  5628  caovord  5629  caovdig  5632  caovdirg  5633  caovmo  5645  ov2gf  5711  map0  6025  enmap2  6068  ce0nnul  6177  ce2  6192  ce2le  6233  tce2  6236  addcdi  6250  muc0or  6252  spaccl  6286  spacind  6287  nchoicelem3  6291  nchoicelem6  6294
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