Theorem oveqd 5472

Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006.)

Hypothesis

Ref	Expression
oveq1d.1	⊢ (φ → A = B)

Assertion

Ref	Expression
oveqd	⊢ (φ → (𝐶A𝐷) = (𝐶B𝐷))

Proof of Theorem oveqd

Step	Hyp	Ref	Expression
1		oveq1d.1	. 2 ⊢ (φ → A = B)
2		oveq 5461	. 2 ⊢ (A = B → (𝐶A𝐷) = (𝐶B𝐷))
3	1, 2	syl 14	1 ⊢ (φ → (𝐶A𝐷) = (𝐶B𝐷))

Syntax hints:   → wi 4   = wceq 1242  (class class class)co 5455

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458

This theorem is referenced by:  oveq123d  5476  csbov12g  5486  ovmpt2dxf  5568  oprssov  5584  ofeq  5656  iseqeq2  8895