Theorem hbl1 104

Description: Inference form of ax-hbl1 103. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypotheses

Ref	Expression
ax-hbl1.1	⊢ A:γ
ax-hbl1.2	⊢ B:α
hbl1.3	⊢ R:∗

Assertion

Ref	Expression
hbl1	⊢ R⊧[(λx:α λx:β AB) = λx:β A]

Proof of Theorem hbl1

Step	Hyp	Ref	Expression
1		hbl1.3	. 2 ⊢ R:∗
2		ax-hbl1.1	. . 3 ⊢ A:γ
3		ax-hbl1.2	. . 3 ⊢ B:α
4	2, 3	ax-hbl1 103	. 2 ⊢ ⊤⊧[(λx:α λx:β AB) = λx:β A]
5	1, 4	a1i 28	1 ⊢ R⊧[(λx:α λx:β AB) = λx:β A]

Syntax hints:  ∗hb 3  kc 5  λkl 6   = ke 7  [kbr 9  ⊧wffMMJ2 11  wffMMJ2t 12

This theorem was proved from axioms:  ax-syl 15  ax-trud 26  ax-hbl1 103

This theorem is referenced by:  clf  115  cbvf  179  axrep  220