Theorem ndsubeqr-P7.22b 848

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

Hypothesis

Ref	Expression
ndsubeqr-P7.22b.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

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

Proof of Theorem ndsubeqr-P7.22b

Step	Hyp	Ref	Expression
1		ndsubeqr-P7.22b.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	subeqr-P5 635	1 ⊢ (𝛾 → (𝑤 = 𝑡 ↔ 𝑤 = 𝑢))

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  ndsubaddd-P7  858  ndsubmultd-P7  859  ndsubeqr-P7.22b.RC  892  ndsubeqr-P7.22b.CL  912  eqtrns-P7  987  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121