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Theorem ax1 203
 Description: Axiom Simp. Axiom A1 of [Margaris] p. 49. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
ax1.1 R:∗
ax1.2 S:∗
Assertion
Ref Expression
ax1 ⊤⊧[R ⇒ [SR]]

Proof of Theorem ax1
StepHypRef Expression
1 wtru 43 . . . . 5 ⊤:∗
2 ax1.1 . . . . 5 R:∗
31, 2simpr 23 . . . 4 (⊤, R)⊧R
4 ax1.2 . . . 4 S:∗
53, 4adantr 55 . . 3 ((⊤, R), S)⊧R
65ex 158 . 2 (⊤, R)⊧[SR]
76ex 158 1 ⊤⊧[R ⇒ [SR]]
 Colors of variables: type var term Syntax hints:  ∗hb 3  ⊤kt 8  [kbr 9  kct 10  ⊧wffMMJ2 11  wffMMJ2t 12   ⇒ tim 121 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-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-distrl 70  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113 This theorem depends on definitions:  df-ov 73  df-an 128  df-im 129 This theorem is referenced by: (None)
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