Theorem axGEN-P7 933

Description: Generalization Rule (ax-GEN 15), Derived from Natural Deduction Rules. †

Hypothesis

Ref	Expression
axGEN-P7.1	⊢ 𝜑

Assertion

Ref	Expression
axGEN-P7	⊢ ∀𝑥𝜑

Proof of Theorem axGEN-P7

Step	Hyp	Ref	Expression
1		axGEN-P7.1	. . 3 ⊢ 𝜑
2	1	nfrthm-P7 926	. 2 ⊢ Ⅎ𝑥𝜑
3	2, 1	nfrgen-P7.RC 929	1 ⊢ ∀𝑥𝜑

Syntax hints:  ∀wff-forall 8

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18  ax-L7 19  ax-L10 27  ax-L11 28  ax-L12 29

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682  df-psub-D6.2 716

This theorem is referenced by:  alli-P7  947  example-E7.1b  1075  nfrzero-P8  1117  nfrvar-P8  1118  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121