Theorem alle-P7.CL 942

Description: Closed Form of alle-P7 941. †

Assertion

Ref	Expression
alle-P7.CL	⊢ (∀𝑥𝜑 → 𝜑)

Proof of Theorem alle-P7.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥𝜑)
2	1	alle-P7 941	1 ⊢ (∀𝑥𝜑 → 𝜑)

Syntax hints:  ∀wff-forall 8   → wff-imp 10

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:  axL4-P7  945  axL4ex-P7  946  allnegex-P7-L1  956  gennfrcl-P7  963  qimeqallhalf-P7  975  dfpsubv-P7  977  axL11-P7  980  alle-P7r.CL  994  gennfr-P8  1079  idempotall-P8  1093  idempotallex-P8  1095  idempotallnall-P8  1097  idempotallnex-P8  1099  qremall-P8  1101