Theorem afveq2 41638

Description: Equality theorem for function value, analogous to fveq1 6303. (Contributed by Alexander van der Vekens, 22-Jul-2017.)

Assertion

Ref	Expression
afveq2	⊢ (𝐴 = 𝐵 → (𝐹'''𝐴) = (𝐹'''𝐵))

Proof of Theorem afveq2

Step	Hyp	Ref	Expression
1		eqidd 2725	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afveq12d 41636	1 ⊢ (𝐴 = 𝐵 → (𝐹'''𝐴) = (𝐹'''𝐵))

Syntax hints:   → wi 4   = wceq 1596  '''cafv 41617

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-rex 3020  df-rab 3023  df-v 3306  df-dif 3683  df-un 3685  df-in 3687  df-ss 3694  df-nul 4024  df-if 4195  df-sn 4286  df-pr 4288  df-op 4292  df-uni 4545  df-br 4761  df-opab 4821  df-xp 5224  df-rel 5225  df-cnv 5226  df-co 5227  df-dm 5228  df-res 5230  df-iota 5964  df-fun 6003  df-fv 6009  df-dfat 41619  df-afv 41620

This theorem is referenced by:  ffnaov  41702