Theorem hbl1 104

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

Hypotheses

Ref	Expression
ax-hbl1.1	|- A:ga
ax-hbl1.2	|- B:al
hbl1.3	|- R:*

Assertion

Ref	Expression
hbl1	|- R |= [(\x:al \x:be AB) = \x:be A]

Proof of Theorem hbl1

Step	Hyp	Ref	Expression
1		hbl1.3	. 2 |- R:*
2		ax-hbl1.1	. . 3 |- A:ga
3		ax-hbl1.2	. . 3 |- B:al
4	2, 3	ax-hbl1 103	. 2 |- T. |= [(\x:al \x:be AB) = \x:be A]
5	1, 4	a1i 28	1 |- R |= [(\x:al \x:be AB) = \x:be A]

Syntax hints:  *hb 3  kc 5  \kl 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