Theorem axgen 197

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

Hypothesis

Ref	Expression
axgen.1	|- T. |= R

Assertion

Ref	Expression
axgen	|- T. |= (A.\x:al R)

Distinct variable group:   al,x

Proof of Theorem axgen

Step	Hyp	Ref	Expression
1		axgen.1	. 2 |- T. |= R
2	1	alrimiv 141	1 |- T. |= (A.\x:al R)

Syntax hints:  kc 5  \kl 6  T.kt 8   |= wffMMJ2 11  A.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)