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Theorem hbl 102

Description: Hypothesis builder for lambda abstraction.

**Assertion**
Ref	Expression
hbl	⊢ R⊧[(λx:α λy:β AB) = λy:β A]

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

**Proof of Theorem hbl**
Step	Hyp	Ref	Expression
1		hbl.1	. . . . 5 ⊢ A:γ
2	1	wl 59	. . . 4 ⊢ λy:β A:(β → γ)
3	2	wl 59	. . 3 ⊢ λx:α λy:β A:(α → (β → γ))
4		hbl.2	. . 3 ⊢ B:α
5	3, 4	wc 45	. 2 ⊢ (λx:α λy:β AB):(β → γ)
6		hbl.3	. . . 4 ⊢ R⊧[(λx:α AB) = A]
7	6	ax-cb1 29	. . 3 ⊢ R:∗
8	1, 4	distrl 84	. . 3 ⊢ ⊤⊧[(λx:α λy:β AB) = λy:β (λx:α AB)]
9	7, 8	a1i 28	. 2 ⊢ R⊧[(λx:α λy:β AB) = λy:β (λx:α AB)]
10	1	wl 59	. . . 4 ⊢ λx:α A:(α → γ)
11	10, 4	wc 45	. . 3 ⊢ (λx:α AB):γ
12	11, 6	leq 81	. 2 ⊢ R⊧[λy:β (λx:α AB) = λy:β A]
13	5, 9, 12	eqtri 85	1 ⊢ R⊧[(λx:α λy:β AB) = λy:β A]

Colors of variables: type var term

Syntax hints: → ht 2 kc 5 λkl 6 = 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 ax-leq 62 ax-distrl 63

This theorem depends on definitions: df-ov 65

This theorem is referenced by: cbvf 167 ax7 196 axrep 207