Theorem ax4 2145

Description: This theorem repeats sp 1747 under the name ax4 2145, so that the metamath program's "verify markup" command will check that it matches axiom scheme ax-4 2135. It is preferred that references to this theorem use the name sp 1747. (Contributed by NM, 18-Aug-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
ax4	|- (A.xph -> ph)

Proof of Theorem ax4

Step	Hyp	Ref	Expression
1		sp 1747	1 |- (A.xph -> ph)

Syntax hints:   -> wi 4  A.wal 1540

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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)