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Theorem ax12olem4 1930
Description: Lemma for ax12o 1934. Construct an intermediate equivalent to ax-12 1925 from two instances of ax-12 1925. (Contributed by NM, 24-Dec-2015.)
Hypotheses
Ref Expression
ax12olem4.1
ax12olem4.2
Assertion
Ref Expression
ax12olem4
Distinct variable groups:   ,,   ,,

Proof of Theorem ax12olem4
StepHypRef Expression
1 ax12olem4.1 . 2
2 ax12olem4.2 . . 3
32ax12olem2 1928 . 2
4 ax12olem3 1929 . 2
51, 3, 4mpbir2an 886 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4  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-6 1729  ax-7 1734  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by:  ax12o  1934
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