Theorem eqid 83

Description: Reflexivity of equality. (Contributed by Mario Carneiro, 7-Oct-2014.)

Hypotheses

Ref	Expression
eqid.1	|- R:*
eqid.2	|- A:al

Assertion

Ref	Expression
eqid	|- R |= [A = A]

Proof of Theorem eqid

Step	Hyp	Ref	Expression
1		weq 41	. 2 |- = :(al -> (al -> *))
2		eqid.2	. 2 |- A:al
3		eqid.1	. . 3 |- R:*
4	2	ax-refl 42	. . 3 |- T. |= (( = A)A)
5	3, 4	a1i 28	. 2 |- R |= (( = A)A)
6	1, 2, 2, 5	dfov2 75	1 |- R |= [A = A]

Syntax hints:  *hb 3  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

This theorem depends on definitions:  df-ov 73

This theorem is referenced by:  ceq1  89  ceq2  90  oveq1  99  oveq12  100  oveq2  101  oveq  102  insti  114  dfan2  154  leqf  181  ax9  212  axrep  220  axpow  221