Theorem wsuceq2 33798

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 2740	. 2 ⊢ 𝑅 = 𝑅
2		eqid 2740	. 2 ⊢ 𝑋 = 𝑋
3		wsuceq123 33796	. 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵 ∧ 𝑋 = 𝑋) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))
4	1, 2, 3	mp3an13 1451	1 ⊢ (𝐴 = 𝐵 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐵, 𝑋))

Syntax hints:   → wi 4   = wceq 1542  wsuccwsuc 33792

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-opab 5142  df-xp 5595  df-cnv 5597  df-dm 5599  df-rn 5600  df-res 5601  df-ima 5602  df-pred 6200  df-sup 9171  df-inf 9172  df-wsuc 33794

This theorem is referenced by: (None)