Theorem eqref-P5 626

Description: Equivalence Property: '=' Reflexivity.

Assertion

Ref	Expression
eqref-P5	⊢ 𝑡 = 𝑡

Proof of Theorem eqref-P5

Dummy variable 𝑥 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax-L7 19	. . 3 ⊢ (𝑥 = 𝑡 → (𝑥 = 𝑡 → 𝑡 = 𝑡))
2	1	rae-P3.26.RC 264	. 2 ⊢ (𝑥 = 𝑡 → 𝑡 = 𝑡)
3		axL6ex-P5 625	. 2 ⊢ ∃𝑥 𝑥 = 𝑡
4	2, 3	exiav-P5.SH 616	1 ⊢ 𝑡 = 𝑡

Syntax hints:  term-obj 1   = wff-equals 6

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

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

This theorem is referenced by:  eqsym-P5  627  ndeqi-P7.21  846