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Metamath Proof Explorer

Theorem xnegeqd

Description: Equality of two extended numbers with -e in front of them. (Contributed by Glauco Siliprandi, 2-Jan-2022)

Ref Expression
Hypothesis xnegeqd.1 ⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion xnegeqd ( 𝜑 → -𝑒 𝐴 = -𝑒 𝐵 )

Proof

Step Hyp Ref Expression
1 xnegeqd.1 ⊢ ( 𝜑 → 𝐴 = 𝐵 )
2 xnegeq ⊢ ( 𝐴 = 𝐵 → -𝑒 𝐴 = -𝑒 𝐵 )
3 1 2 syl ⊢ ( 𝜑 → -𝑒 𝐴 = -𝑒 𝐵 )