Theorem nfrthm-P7 926

Description: Every Variable is ENF in a Theorem. †

Hypothesis

Ref	Expression
nfrthm-P7.1	⊢ 𝜑

Assertion

Ref	Expression
nfrthm-P7	⊢ Ⅎ𝑥𝜑

Proof of Theorem nfrthm-P7

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑥⊤
2		nfrthm-P7.1	. . . 4 ⊢ 𝜑
3	2	thmeqtrue-P4.21a 442	. . 3 ⊢ (𝜑 ↔ ⊤)
4	3	ndnfrleq-P7.11.RC 882	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥⊤)
5	1, 4	bimpr-P4.RC 534	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:  ⊤wff-true 153  Ⅎwff-nfree 681

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-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

This theorem is referenced by:  axGEN-P7  933  nfrthm-P8  1107