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Theorem 2i3 254
Description: Join both sides with Kalmbach implication. (Contributed by NM, 2-Nov-1997.)
Hypotheses
Ref Expression
2i3.1 a = b
2i3.2 c = d
Assertion
Ref Expression
2i3 (a3 c) = (b3 d)

Proof of Theorem 2i3
StepHypRef Expression
1 2i3.2 . . 3 c = d
21li3 252 . 2 (a3 c) = (a3 d)
3 2i3.1 . . 3 a = b
43ri3 253 . 2 (a3 d) = (b3 d)
52, 4ax-r2 36 1 (a3 c) = (b3 d)
Colors of variables: term
Syntax hints:   = wb 1  3 wi3 14
This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i3 46
This theorem is referenced by:  i32i3  540  u3lemax4  796
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