Theorem eqsym-P5.CL.SYM 629

Description: Closed Symmetric Form of eqsym-P5 627.

Assertion

Ref	Expression
eqsym-P5.CL.SYM	⊢ (𝑡 = 𝑢 ↔ 𝑢 = 𝑡)

Proof of Theorem eqsym-P5.CL.SYM

Step	Hyp	Ref	Expression
1		eqsym-P5.CL 628	. 2 ⊢ (𝑡 = 𝑢 → 𝑢 = 𝑡)
2		eqsym-P5.CL 628	. 2 ⊢ (𝑢 = 𝑡 → 𝑡 = 𝑢)
3	1, 2	rcp-NDBII0 239	1 ⊢ (𝑡 = 𝑢 ↔ 𝑢 = 𝑡)

Syntax hints:   = wff-equals 6   ↔ wff-bi 104

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:  eqtrns-P5  630  subeqr-P5-L1  634  subeqr-P5  635  subelofl-P5  638  subelofr-P5  640  cbvallv-P5  659  specw-P5  661  lemma-L5.04a  667  exi-P6  718  cbvall-P6  751