Theorem insti 114

Description: Instantiate a theorem with a new term. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypotheses

Ref	Expression
insti.1	|- C:al
insti.2	|- B:*
insti.3	|- R |= A
insti.4	|- T. |= [(\x:al By:al) = B]
insti.5	|- [x:al = C] |= [A = B]

Assertion

Ref	Expression
insti	|- R |= B

Distinct variable groups:   x,y,R   y,B

Proof of Theorem insti

Step	Hyp	Ref	Expression
1		insti.3	. 2 |- R |= A
2		insti.4	. 2 |- T. |= [(\x:al By:al) = B]
3	1	ax-cb1 29	. . 3 |- R:*
4		wv 64	. . 3 |- y:al:al
5	3, 4	ax-17 105	. 2 |- T. |= [(\x:al Ry:al) = R]
6		insti.5	. 2 |- [x:al = C] |= [A = B]
7	6	ax-cb1 29	. . 3 |- [x:al = C]:*
8	7, 3	eqid 83	. 2 |- [x:al = C] |= [R = R]
9	1, 2, 5, 6, 8	ax-inst 113	1 |- R |= B

Syntax hints:  tv 1  *hb 3  kc 5  \kl 6   = ke 7  T.kt 8  [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-wv 63  ax-wov 71  ax-17 105  ax-inst 113

This theorem depends on definitions:  df-ov 73

This theorem is referenced by:  clf  115  exlimdv  167  cbvf  179  exlimd  183