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Theorem ceq1 89
 Description: Equality theorem for combination. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
ceq12.1 F:(αβ)
ceq12.2 A:α
ceq12.3 R⊧[F = T]
Assertion
Ref Expression
ceq1 R⊧[(FA) = (TA)]

Proof of Theorem ceq1
StepHypRef Expression
1 ceq12.1 . 2 F:(αβ)
2 ceq12.2 . 2 A:α
3 ceq12.3 . 2 R⊧[F = T]
43ax-cb1 29 . . 3 R:∗
54, 2eqid 83 . 2 R⊧[A = A]
61, 2, 3, 5ceq12 88 1 R⊧[(FA) = (TA)]
 Colors of variables: type var term Syntax hints:   → ht 2  kc 5   = 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-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wov 71  ax-eqtypi 77 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  hbxfrf  107  ovl  117  alval  142  exval  143  euval  144  notval  145  ax4g  149  dfan2  154  eta  178  ac  197  ax14  217  axrep  220  axpow  221  axun  222
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