Theorem ndsubelofr-P7.23b.RC 895

Description: Inference Form of ndsubelofr-P7.23b 850. †

Hypothesis

Ref	Expression
ndsubelofr-P7.23b.RC.1	⊢ 𝑡 = 𝑢

Assertion

Ref	Expression
ndsubelofr-P7.23b.RC	⊢ (𝑤 ∈ 𝑡 ↔ 𝑤 ∈ 𝑢)

Proof of Theorem ndsubelofr-P7.23b.RC

Step	Hyp	Ref	Expression
1		ndsubelofr-P7.23b.RC.1	. . . 4 ⊢ 𝑡 = 𝑢
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝑡 = 𝑢)
3	2	ndsubelofr-P7.23b 850	. 2 ⊢ (⊤ → (𝑤 ∈ 𝑡 ↔ 𝑤 ∈ 𝑢))
4	3	ndtruee-P3.18 183	1 ⊢ (𝑤 ∈ 𝑡 ↔ 𝑤 ∈ 𝑢)

Syntax hints:   = wff-equals 6   ∈ wff-elemof 7   ↔ 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  ax-L8-inr 21

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)