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Theorem ax1 190
Description: Axiom Simp. Axiom A1 of [Margaris] p. 49.
Hypotheses
Ref Expression
ax1.1 |- R:*
ax1.2 |- S:*
Assertion
Ref Expression
ax1 |- T. |= [R ==> [S ==> R]]
Proof of Theorem ax1
StepHypRef Expression
1 wtru 40 . . . . 5 |- T.:*
2 ax1.1 . . . . 5 |- R:*
31, 2simpr 23 . . . 4 |- (T., R) |= R
4 ax1.2 . . . 4 |- S:*
53, 4adantr 50 . . 3 |- ((T., R), S) |= R
65ex 148 . 2 |- (T., R) |= [S ==> R]
76ex 148 1 |- T. |= [R ==> [S ==> R]]
Colors of variables: type var term
Syntax hints:  *hb 3  T.kt 8  [kbr 9  kct 10   |= wffMMJ2 11  wffMMJ2t 12   ==> tim 111
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ded 43  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-distrl 63  ax-hbl1 93  ax-17 95  ax-inst 103
This theorem depends on definitions:  df-ov 65  df-an 118  df-im 119
This theorem is referenced by: (None)
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