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Theorem ss2abi 3338
 Description: Inference of abstraction subclass from implication. (Contributed by NM, 31-Mar-1995.)
Hypothesis
Ref Expression
ss2abi.1 (φψ)
Assertion
Ref Expression
ss2abi {x φ} {x ψ}

Proof of Theorem ss2abi
StepHypRef Expression
1 ss2ab 3334 . 2 ({x φ} {x ψ} ↔ x(φψ))
2 ss2abi.1 . 2 (φψ)
31, 2mpgbir 1550 1 {x φ} {x ψ}
 Colors of variables: wff setvar class Syntax hints:   → wi 4  {cab 2339   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  abssi  3341  rabssab  3352  imassrn  5009  mapsspm  6021
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