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Theorem ceq1 79
Description: Equality theorem for combination.
Hypotheses
Ref Expression
ceq12.1 |- F:(al -> be)
ceq12.2 |- A:al
ceq12.3 |- R |= [F = T]
Assertion
Ref Expression
ceq1 |- R |= [(FA) = (TA)]
Proof of Theorem ceq1
StepHypRef Expression
1 ceq12.1 . 2 |- F:(al -> be)
2 ceq12.2 . 2 |- A:al
3 ceq12.3 . 2 |- R |= [F = T]
43ax-cb1 29 . . 3 |- R:*
54, 2eqid 73 . 2 |- R |= [A = A]
61, 2, 3, 5ceq12 78 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-refl 39  ax-eqmp 42  ax-ceq 46
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  hbxfrf  97  ovl  107  alval  132  exval  133  euval  134  notval  135  ax4g  139  dfan2  144  eta  166  ac  184  ax14  204  axrep  207  axpow  208  axun  209
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