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Theorem bnj1292 31704
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1292.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj1292 𝐴𝐵

Proof of Theorem bnj1292
StepHypRef Expression
1 bnj1292.1 . 2 𝐴 = (𝐵𝐶)
2 inss1 4125 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2eqsstri 3922 1 𝐴𝐵
 Colors of variables: wff setvar class Syntax hints:   = wceq 1522   ∩ cin 3858   ⊆ wss 3859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-v 3439  df-in 3866  df-ss 3874 This theorem is referenced by:  bnj1253  31903  bnj1286  31905  bnj1280  31906  bnj1296  31907
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