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Theorem oveq1 89
Description: Equality theorem for binary operation.
Hypotheses
Ref Expression
oveq.1 |- F:(al -> (be -> ga))
oveq.2 |- A:al
oveq.3 |- B:be
oveq1.4 |- R |= [A = C]
Assertion
Ref Expression
oveq1 |- R |= [[AFB] = [CFB]]
Proof of Theorem oveq1
StepHypRef Expression
1 oveq.1 . 2 |- F:(al -> (be -> ga))
2 oveq.2 . 2 |- A:al
3 oveq.3 . 2 |- B:be
4 oveq1.4 . . . 4 |- R |= [A = C]
54ax-cb1 29 . . 3 |- R:*
65, 1eqid 73 . 2 |- R |= [F = F]
75, 3eqid 73 . 2 |- R |= [B = B]
81, 2, 3, 6, 4, 7oveq123 88 1 |- R |= [[AFB] = [CFB]]
Colors of variables: type var term
Syntax hints:   -> ht 2   = ke 7  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ceq 46
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  alval  132  exval  133  euval  134  notval  135  imval  136  orval  137  anval  138  exlimdv  157  ax4e  158  exlimd  171  ac  184  exmid  186  ax10  200  axrep  207
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