Theorem ndsubeql-P7.22a 847

Description: Natural Deduction: Equality Substitution Rule (left).

Hypothesis

Ref	Expression
ndsubeql-P7.22a.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

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

Proof of Theorem ndsubeql-P7.22a

Step	Hyp	Ref	Expression
1		ndsubeql-P7.22a.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	subeql-P5 632	1 ⊢ (𝛾 → (𝑡 = 𝑤 ↔ 𝑢 = 𝑤))

Syntax hints:   = wff-equals 6   → wff-imp 10   ↔ 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:  ndsubeqd-P7  856  ndsubeql-P7.22a.RC  891  ndsubeql-P7.22a.CL  911  eqsym-P7  936  example-E7.1a  1074