Theorem nd5 4914

Description: A lemma for proving conditionless ZFC axioms.

Assertion

Ref	Expression
nd5	|- (-. A.y y = x -> (z = y -> A.x z = y))

Distinct variable group:   x,z

Proof of Theorem nd5

Step	Hyp	Ref	Expression
1		dveeq2 1208	. 2 |- (-. A.x x = y -> (z = y -> A.x z = y))
2	1	nalequcoms 1140	1 |- (-. A.y y = x -> (z = y -> A.x z = y))

Syntax hints:  -. wn 2   -> wi 3  A.wal 951   = wceq 953

This theorem is referenced by:  axrepndlem1 4916  axrepndlem2 4917  axunnd 4920  axpowndlem2 4922  axpowndlem4 4924  axregndlem2 4927  axinfndlem1 4929  axinfnd 4930  axacndlem4 4934  axacndlem5 4935  axacnd 4936

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136

This theorem depends on definitions:  df-bi 147  df-an 225

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