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Theorem ceq1 79

Description: Equality theorem for combination.

Hypotheses

Ref	Expression
ceq12.1	⊢ F:(α → β)
ceq12.2	⊢ A:α
ceq12.3	⊢ R⊧[F = T]

Assertion

Ref	Expression
ceq1	⊢ R⊧[(FA) = (TA)]

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Proof of Theorem ceq1

Step	Hyp	Ref	Expression
1		ceq12.1	. 2 ⊢ F:(α → β)
2		ceq12.2	. 2 ⊢ A:α
3		ceq12.3	. 2 ⊢ R⊧[F = T]
4	3	ax-cb1 29	. . 3 ⊢ R:∗
5	4, 2	eqid 73	. 2 ⊢ R⊧[A = A]
6	1, 2, 3, 5	ceq12 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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