Theorem hbth 99

Description: Hypothesis builder for a theorem.

Hypotheses

Ref	Expression
hbth.1	⊢ B:α
hbth.2	⊢ R⊧A

Assertion

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

Distinct variable group:   x,R

Proof of Theorem hbth

Step	Hyp	Ref	Expression
1		hbth.2	. . 3 ⊢ R⊧A
2	1	ax-cb2 30	. 2 ⊢ A:∗
3		hbth.1	. 2 ⊢ B:α
4		wtru 40	. . 3 ⊢ ⊤:∗
5	1	eqtru 76	. . 3 ⊢ R⊧[⊤ = A]
6	4, 5	eqcomi 70	. 2 ⊢ R⊧[A = ⊤]
7	1	ax-cb1 29	. . 3 ⊢ R:∗
8	4, 3, 7	a17i 96	. 2 ⊢ R⊧[(λx:α ⊤B) = ⊤]
9	2, 3, 6, 8	hbxfr 98	1 ⊢ R⊧[(λx:α AB) = A]

Syntax hints:  ∗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-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ded 43  ax-ceq 46  ax-leq 62  ax-17 95

This theorem depends on definitions:  df-ov 65

This theorem is referenced by:  ax4g  139