Theorem axgen 210

Description: Rule of Generalization. See e.g. Rule 2 of [Hamilton] p. 74. (Contributed by Mario Carneiro, 10-Oct-2014.)

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 151	1 |- T. |= (A.\x:al R)

Syntax hints:  kc 5  \kl 6  T.kt 8   |= wffMMJ2 11  A.tal 122

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-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113

This theorem depends on definitions:  df-ov 73  df-al 126

This theorem is referenced by: (None)