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Theorem hbth 109
 Description: Hypothesis builder for a theorem. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
hbth.1 B:α
hbth.2 RA
Assertion
Ref Expression
hbth R⊧[(λx:α AB) = A]
Distinct variable group:   x,R

Proof of Theorem hbth
StepHypRef Expression
1 hbth.2 . . 3 RA
21ax-cb2 30 . 2 A:∗
3 hbth.1 . 2 B:α
4 wtru 43 . . 3 ⊤:∗
51eqtru 86 . . 3 R⊧[⊤ = A]
64, 5eqcomi 79 . 2 R⊧[A = ⊤]
71ax-cb1 29 . . 3 R:∗
84, 3, 7a17i 106 . 2 R⊧[(λx:αB) = ⊤]
92, 3, 6, 8hbxfr 108 1 R⊧[(λx:α AB) = A]
 Colors of variables: type var term 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-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wl 65  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-17 105 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  ax4g  149
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