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Theorem elmpt2cl2 6527
 Description: If a two-parameter class is not empty, the second argument is in its nominal domain. (Contributed by FL, 15-Oct-2012.) (Revised by Stefan O'Rear, 7-Mar-2015.)
Hypothesis
Ref Expression
elmpt2cl.f
Assertion
Ref Expression
elmpt2cl2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)

Proof of Theorem elmpt2cl2
StepHypRef Expression
1 elmpt2cl.f . . 3
21elmpt2cl 6525 . 2
32simprd 464 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437   wcel 1870  (class class class)co 6305   cmpt2 6307 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-8 1872  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pow 4603  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-opab 4485  df-xp 4860  df-dm 4864  df-iota 5565  df-fv 5609  df-ov 6308  df-oprab 6309  df-mpt2 6310 This theorem is referenced by:  iccssico2  11708  swrdcl  12760  mhmrcl2  16537  rhmrcl2  17883  mpfrcl  18676  cncfrss2  21820  relowlpssretop  31501  pfxcl  38317
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