Theorem axL6-P7 961

Description: ax-L6 18 Derived From Natural Deduction Rules. †

'𝑥' cannot occur in '𝑡'.

Assertion

Ref	Expression
axL6-P7	⊢ ¬ ∀𝑥 ¬ 𝑥 = 𝑡

Distinct variable group:   𝑡,𝑥

Proof of Theorem axL6-P7

Step	Hyp	Ref	Expression
1		axL6ex-P7 925	. 2 ⊢ ∃𝑥 𝑥 = 𝑡
2		dfexistsint-P7 960	. 2 ⊢ (∃𝑥 𝑥 = 𝑡 → ¬ ∀𝑥 ¬ 𝑥 = 𝑡)
3	1, 2	rcp-NDIME0 228	1 ⊢ ¬ ∀𝑥 ¬ 𝑥 = 𝑡

Syntax hints:  term-obj 1   = wff-equals 6  ∀wff-forall 8  ¬ wff-neg 9  ∃wff-exists 595

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-false-D2.5 158  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682  df-psub-D6.2 716

This theorem is referenced by: (None)