axgen - Higher-Order Logic Explorer

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Theorem axgen 197

Description: Rule of Generalization. See e.g. Rule 2 of [Hamilton] p. 74.

**Hypothesis**
Ref	Expression
axgen.1	⊢ ⊤⊧R

**Assertion**
Ref	Expression
axgen	⊢ ⊤⊧(∀λx:α R)

Distinct variable group: α,x

**Proof of Theorem axgen**
Step	Hyp	Ref	Expression
1		axgen.1	. 2 ⊢ ⊤⊧R
2	1	alrimiv 141	1 ⊢ ⊤⊧(∀λx:α R)

Colors of variables: type var term

Syntax hints: kc 5 λkl 6 ⊤kt 8 ⊧wffMMJ2 11 ∀tal 112

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-beta 60 ax-distrc 61 ax-leq 62 ax-hbl1 93 ax-17 95 ax-inst 103

This theorem depends on definitions: df-ov 65 df-al 116

This theorem is referenced by: (None)