Theorem nfa1-o 2166

Description: x is not free in A.xph. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfa1-o	|- F/xA.xph

Proof of Theorem nfa1-o

Step	Hyp	Ref	Expression
1		hba1-o 2149	. 2 |- (A.xph -> A.xA.xph)
2	1	nfi 1551	1 |- F/xA.xph

Syntax hints:  A.wal 1540   F/wnf 1544

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-4 2135  ax-5o 2136  ax-6o 2137

This theorem depends on definitions:  df-bi 177  df-nf 1545

This theorem is referenced by:  ax10-16  2190  ax11eq  2193  ax11el  2194  ax11v2-o  2201