Theorem ndsubeql-P7.22a.RC 891

Description: Inference Form of ndsubeql-P7.22a 847. †

Hypothesis

Ref	Expression
ndsubeql-P7.22a.RC.1	⊢ 𝑡 = 𝑢

Assertion

Ref	Expression
ndsubeql-P7.22a.RC	⊢ (𝑡 = 𝑤 ↔ 𝑢 = 𝑤)

Proof of Theorem ndsubeql-P7.22a.RC

Step	Hyp	Ref	Expression
1		ndsubeql-P7.22a.RC.1	. . . 4 ⊢ 𝑡 = 𝑢
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝑡 = 𝑢)
3	2	ndsubeql-P7.22a 847	. 2 ⊢ (⊤ → (𝑡 = 𝑤 ↔ 𝑢 = 𝑤))
4	3	ndtruee-P3.18 183	1 ⊢ (𝑡 = 𝑤 ↔ 𝑢 = 𝑤)

Syntax hints:   = wff-equals 6   ↔ wff-bi 104  ⊤wff-true 153

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: (None)