Theorem bnj1213 33809

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 3981	1 ⊢ (𝜃 → 𝑥 ∈ 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2107   ⊆ wss 3949

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966

This theorem is referenced by:  bnj1212  33810  bnj1173  34013  bnj1296  34032  bnj1408  34047  bnj1452  34063  bnj1523  34082