Theorem axL6ex-P7 925

Description: Existential Form of ax-L6 18, Derived from Natural Deduction Rules. †

'𝑥' cannot occur in '𝑡'.

Assertion

Ref	Expression
axL6ex-P7	⊢ ∃𝑥 𝑥 = 𝑡

Distinct variable group:   𝑡,𝑥

Proof of Theorem axL6ex-P7

Step	Hyp	Ref	Expression
1		ndeqi-P7.21 846	. . 3 ⊢ 𝑡 = 𝑡
2		lemma-L7.01a 924	. . 3 ⊢ ([𝑡 / 𝑥] 𝑥 = 𝑡 ↔ 𝑡 = 𝑡)
3	1, 2	bimpr-P4.RC 534	. 2 ⊢ [𝑡 / 𝑥] 𝑥 = 𝑡
4	3	ndexi-P7.19.RC 886	1 ⊢ ∃𝑥 𝑥 = 𝑡

Syntax hints:  term-obj 1   = wff-equals 6  ∃wff-exists 595  [wff-psub 714

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  df-psub-D6.2 716

This theorem is referenced by:  psubnfrv-P7  927  psubinv-P7  939  lemma-L7.02a-L1  943  axL6-P7  961  lemma-L7.03  962  dfpsubv-P7  977  example-E7.1b  1075  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121