Theorem axL6ex-P5 625

Description: Existential Form of ax-L6 18.

Assertion

Ref	Expression
axL6ex-P5	⊢ ∃𝑥 𝑥 = 𝑡

Distinct variable group:   𝑡,𝑥

Proof of Theorem axL6ex-P5

Step	Hyp	Ref	Expression
1		ax-L6 18	. 2 ⊢ ¬ ∀𝑥 ¬ 𝑥 = 𝑡
2		df-exists-D5.1 596	. 2 ⊢ (∃𝑥 𝑥 = 𝑡 ↔ ¬ ∀𝑥 ¬ 𝑥 = 𝑡)
3	1, 2	bimpr-P4.RC 534	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-L6 18

This theorem depends on definitions:  df-bi-D2.1 107  df-true-D2.4 155  df-exists-D5.1 596

This theorem is referenced by:  eqref-P5  626  lemma-L5.02a  653  solvesub-P6a  704  eqmiddle-P6  708  exi-P6  718  exipsub-P6  720  lemma-L6.02a  726  lemma-L6.04a  749  lemma-L6.07a-L2  771  spliteq-P6  776  splitelof-P6  778  nfrsucc-P6  780  nfradd-P6  781  nfrmult-P6  782  psubnfr-P6  784  psubsuccv-P6-L1  805  psubaddv-P6-L1  807  psubmultv-P6-L1  809