Theorem wsuceq2 35780

Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018.)

Assertion

Ref	Expression
wsuceq2	⊢ (𝐴 = 𝐵 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))

Proof of Theorem wsuceq2

Step	Hyp	Ref	Expression
1		eqid 2735	. 2 ⊢ 𝑅 = 𝑅
2		eqid 2735	. 2 ⊢ 𝑋 = 𝑋
3		wsuceq123 35778	. 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵 ∧ 𝑋 = 𝑋) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))
4	1, 2, 3	mp3an13 1454	1 ⊢ (𝐴 = 𝐵 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))

Syntax hints:   → wi 4   = wceq 1540  wsuccwsuc 35774

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-ral 3052  df-rex 3061  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-in 3933  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-opab 5182  df-xp 5660  df-cnv 5662  df-dm 5664  df-rn 5665  df-res 5666  df-ima 5667  df-pred 6290  df-sup 9452  df-inf 9453  df-wsuc 35776

This theorem is referenced by: (None)