Theorem ssidd 3060

Description: Weakening of ssid 3059. (Contributed by BJ, 1-Sep-2022.)

Assertion

Ref	Expression
ssidd	⊢ (𝜑 → 𝐴 ⊆ 𝐴)

Proof of Theorem ssidd

Step	Hyp	Ref	Expression
1		ssid 3059	. 2 ⊢ 𝐴 ⊆ 𝐴
2	1	a1i 9	1 ⊢ (𝜑 → 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3013

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-11 1449  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-in 3019  df-ss 3026

This theorem is referenced by:  isum  10943  fsum3ser  10955  fsumcl  10958  restopn2  12050