Theorem oveq123i 5958

Description: Equality inference for operation value. (Contributed by FL, 11-Jul-2010.)

Hypotheses

Ref	Expression
oveq123i.1	⊢ 𝐴 = 𝐶
oveq123i.2	⊢ 𝐵 = 𝐷
oveq123i.3	⊢ 𝐹 = 𝐺

Assertion

Ref	Expression
oveq123i	⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

Proof of Theorem oveq123i

Step	Hyp	Ref	Expression
1		oveq123i.1	. . 3 ⊢ 𝐴 = 𝐶
2		oveq123i.2	. . 3 ⊢ 𝐵 = 𝐷
3	1, 2	oveq12i 5956	. 2 ⊢ (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4		oveq123i.3	. . 3 ⊢ 𝐹 = 𝐺
5	4	oveqi 5957	. 2 ⊢ (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
6	3, 5	eqtri 2226	1 ⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

Syntax hints:   = wceq 1373  (class class class)co 5944

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-uni 3851  df-br 4045  df-iota 5232  df-fv 5279  df-ov 5947

This theorem is referenced by: (None)