Theorem oveq12i 5524

Description: Equality inference for operation value. (Contributed by NM, 28-Feb-1995.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)

Hypotheses

Ref	Expression
oveq1i.1	|- A = B
oveq12i.2	|- C = D

Assertion

Ref	Expression
oveq12i	|- ( A F C ) = ( B F D )

Proof of Theorem oveq12i

Step	Hyp	Ref	Expression
1		oveq1i.1	. 2 |- A = B
2		oveq12i.2	. 2 |- C = D
3		oveq12 5521	. 2 |- ( ( A = B /\ C = D ) -> ( A F C ) = ( B F D ) )
4	1, 2, 3	mp2an 402	1 |- ( A F C ) = ( B F D )

Syntax hints:   = wceq 1243  (class class class)co 5512

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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515

This theorem is referenced by:  oveq123i  5526  1lt2nq  6504  halfnqq  6508  caucvgprprlemnbj  6791  caucvgprprlemaddq  6806  m1p1sr  6845  m1m1sr  6846  axi2m1  6949  negdii  7295  3t3e9  8072  8th4div3  8144  halfpm6th  8145  numma  8398  4t3lem  8438  sqdivapi  9337  i4  9355  binom2i  9360  cji  9502