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Metamath Proof Explorer

Theorem bnj551

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj551 ⊢ m = suc ⁡ p ∧ m = suc ⁡ i → p = i

Proof

Step Hyp Ref Expression
1 eqtr2 ⊢ m = suc ⁡ p ∧ m = suc ⁡ i → suc ⁡ p = suc ⁡ i
2 suc11reg ⊢ suc ⁡ p = suc ⁡ i ↔ p = i
3 1 2 sylib ⊢ m = suc ⁡ p ∧ m = suc ⁡ i → p = i