Theorem a17i 106

Description: Inference form of ax-17 105. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypotheses

Ref	Expression
ax-17.1	⊢ A:β
ax-17.2	⊢ B:α
a17i.3	⊢ R:∗

Assertion

Ref	Expression
a17i	⊢ R⊧[(λx:α AB) = A]

Distinct variable group:   x,A

Proof of Theorem a17i

Step	Hyp	Ref	Expression
1		a17i.3	. 2 ⊢ R:∗
2		ax-17.1	. . 3 ⊢ A:β
3		ax-17.2	. . 3 ⊢ B:α
4	2, 3	ax-17 105	. 2 ⊢ ⊤⊧[(λx:α AB) = A]
5	1, 4	a1i 28	1 ⊢ R⊧[(λx:α AB) = 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-17 105

This theorem is referenced by:  hbth  109  clf  115  hbct  155  axun  222