Theorem ax10lem6 1943

Description: Lemma for ax10 1944. Similar to ax10o 1952 but with reversed antecedent. (Contributed by NM, 25-Jul-2015.)

Assertion

Ref	Expression
ax10lem6	|- (A.y y = x -> (A.xph -> A.yph))

Proof of Theorem ax10lem6

Step	Hyp	Ref	Expression
1		ax-11 1746	. . 3 |- (y = x -> (A.xph -> A.y(y = x -> ph)))
2	1	sps 1754	. 2 |- (A.y y = x -> (A.xph -> A.y(y = x -> ph)))
3		pm2.27 35	. . 3 |- (y = x -> ((y = x -> ph) -> ph))
4	3	al2imi 1561	. 2 |- (A.y y = x -> (A.y(y = x -> ph) -> A.yph))
5	2, 4	syld 40	1 |- (A.y y = x -> (A.xph -> A.yph))

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:  ax10  1944