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Theorem insti 114
 Description: Instantiate a theorem with a new term. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
insti.1 C:α
insti.2 B:∗
insti.3 RA
insti.4 ⊤⊧[(λx:α By:α) = B]
insti.5 [x:α = C]⊧[A = B]
Assertion
Ref Expression
insti RB
Distinct variable groups:   x,y,R   y,B

Proof of Theorem insti
StepHypRef Expression
1 insti.3 . 2 RA
2 insti.4 . 2 ⊤⊧[(λx:α By:α) = B]
31ax-cb1 29 . . 3 R:∗
4 wv 64 . . 3 y:α:α
53, 4ax-17 105 . 2 ⊤⊧[(λx:α Ry:α) = R]
6 insti.5 . 2 [x:α = C]⊧[A = B]
76ax-cb1 29 . . 3 [x:α = C]:∗
87, 3eqid 83 . 2 [x:α = C]⊧[R = R]
91, 2, 5, 6, 8ax-inst 113 1 RB
 Colors of variables: type var term Syntax hints:  tv 1  ∗hb 3  kc 5  λkl 6   = ke 7  ⊤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
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