New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  p6eqd GIF version

Theorem p6eqd 4240
 Description: Equality deduction for the P6 operation. (Contributed by SF, 12-Jan-2015.)
Hypothesis
Ref Expression
p6eqd.1 (φA = B)
Assertion
Ref Expression
p6eqd (φP6 A = P6 B)

Proof of Theorem p6eqd
StepHypRef Expression
1 p6eqd.1 . 2 (φA = B)
2 p6eq 4238 . 2 (A = BP6 A = P6 B)
31, 2syl 15 1 (φP6 A = P6 B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   P6 cp6 4178 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  df-p6 4191 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator