Theorem bnj1213 34643

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

Hypotheses

Ref	Expression
bnj1213.1	⊢ 𝐴 ⊆ 𝐵
bnj1213.2	⊢ (𝜃 → 𝑥 ∈ 𝐴)

Assertion

Ref	Expression
bnj1213	⊢ (𝜃 → 𝑥 ∈ 𝐵)

Proof of Theorem bnj1213

Step	Hyp	Ref	Expression
1		bnj1213.1	. 2 ⊢ 𝐴 ⊆ 𝐵
2		bnj1213.2	. 2 ⊢ (𝜃 → 𝑥 ∈ 𝐴)
3	1, 2	sselid 3977	1 ⊢ (𝜃 → 𝑥 ∈ 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2099   ⊆ wss 3947

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1775  df-clel 2803  df-ss 3964

This theorem is referenced by:  bnj1212  34644  bnj1173  34847  bnj1296  34866  bnj1408  34881  bnj1452  34897  bnj1523  34916